@Article{ Di-Pietro.Mendez.ea:25, title = {A discrete {de Rham} discretization of interface diffusion problems with application to the {Leaky Dielectric Model}}, author = {Di Pietro, D. A. and Mendez, S. and Spadotto, A. E.}, year = {2025}, journal = {J. Comput. Phys.}, volume = {530}, pages = {113920}, doi = {10.1016/j.jcp.2025.113920}, hal = {hal-04706374}, eprint = {2409.15042}, archiveprefix = {arXiv}, primaryclass = {math.NA}, keywords = {prex2,nemesis} } @Misc{ Beirao-da-Veiga.Di-Pietro.ea:25, author = {Beir\~{a}o da Veiga, L. and Di Pietro, D. A. and Droniou, J. and Haile, K. B. and Radley, T. J.}, title = {A {Reynolds}-semi-robust method with hybrid velocity and pressure for the unsteady incompressible {Navier--Stokes} equations}, month = {2}, year = {2025}, eprint = {2502.15293}, archiveprefix = {arXiv}, primaryclass = {math.NA}, keywords = {prex2,nemesis} } @Article{ Botti.Botti.ea:25, author = {Botti, L. and Botti, M. and Di Pietro, D. A., and Massa, F. C.}, title = {Stability, convergence, and pressure-robustness of numerical schemes for incompressible flows with hybrid velocity and pressure}, year = {2025}, journal = {Math. Comp.}, note = {Published online}, doi = {10.1090/mcom/4049}, hal = {hal-04552438}, eprint = {2404.12732}, archiveprefix = {arXiv}, primaryclass = {math.NA}, keywords = {prex2,nemesis} } @Misc{ Di-Pietro.Droniou.ea:25, title = {Uniform Poincar\'{e} inequalities for the discrete de Rham complex of differential forms}, author = {Di Pietro, D. A. and Droniou, J. and Hanot, M.-L. and Pitassi, S.}, year = {2025}, month = {1}, hal = {hal-04914811}, eprint = {2501.16116}, archiveprefix = {arXiv}, primaryclass = {math.NA}, keywords = {prex2,nemesis,effect} } @Article{ Castanon-Quiroz.Di-Pietro:25, title = {A {Reynolds}-semi-robust and pressure-robust {Hybrid High-Order} method for the time dependent incompressible {Navier--Stokes} equations}, author = {Casta\~{n}\'{o}n Quiroz, D. and Di Pietro, D. A.}, journal = {Comput. Meth. Appl. Mech. Engrg.}, year = {2025}, volume = {436}, pages = {117660}, doi = {10.1016/j.cma.2024.117660}, hal = {hal-04693813}, eprint = {2409.07037}, archiveprefix = {arXiv}, primaryclass = {math.NA}, keywords = {prex2,nemesis} } @Article{ Bonaldi.Di-Pietro.ea:25, title = {An exterior calculus framework for polytopal methods}, author = {Bonaldi, F. and Di Pietro, D. A. and Droniou, J. and Hu, K.}, journal = {J. Eur. Math. Soc.}, year = {2025}, doi = {10.4171/JEMS/1602}, hal = {hal-04037653}, eprint = {2303.11093}, archiveprefix = {arXiv}, primaryclass = {math.NA}, note = {Accepted for publication}, keywords = {prex2,nemesis} } @Article{ Di-Pietro.Hanot:24, title = {Uniform Poincar\'{e} inequalities for the Discrete de Rham complex on general domains}, author = {Di Pietro, D. A. and Hanot, M.-L.}, year = {2024}, journal = {Results Appl. Math.}, volume = {23}, number = {100496}, doi = {10.1016/j.rinam.2024.100496}, url = {https://authors.elsevier.com/sd/article/S2590-0374(24)00066-9}, hal = {hal-04220112}, eprint = {2309.15667}, archiveprefix = {arXiv}, primaryclass = {math.NA}, keywords = {prex2,rhamnus,nemesis} } @InProceedings{ Cockburn.Di-Pietro.ea:24, title = {Bridging the {Hybrid High-Order} and {Hybridizable Discontinuous Galerkin} methods: {Summary}}, author = {Cockburn, B. and Di Pietro, D. A. and Ern, A.}, booktitle = {Frontiers of Science Awards for Math/TCIS/Phys}, publisher = {International Press}, year = {2024}, hal = {hal-04680610}, keywords = {prex2} } @Article{ Di-Pietro.Hanot:24*1, title = {A discrete three-dimensional divdiv complex on polyhedral meshes with application to a mixed formulation of the biharmonic problem}, author = {Di Pietro, D. A. and Hanot, M.-L.}, year = {2024}, journal = {Math. Models Methods Appl. Sci.}, volume = {34}, number = {9}, pages = {1597--1648}, doi = {10.1142/S0218202524500313}, hal = {hal-04093192}, eprint = {2305.05729}, archiveprefix = {arXiv}, primaryclass = {math.NA}, keywords = {prex2,anr-mrsei,rhamnus} } @Article{ Beirao-da-Veiga.Di-Pietro.ea:24, author = {Beir\~{a}o da Veiga, L. and Di Pietro, D. A. and Haile, K. B.}, title = {A {P\'{e}clet}-robust discontinuous {Galerkin} method for nonlinear diffusion with advection}, year = {2024}, journal = {Math. Models Methods Appl. Sci.}, volume = {34}, number = {9}, pages = {1781--1807}, doi = {10.1142/S0218202524500350}, hal = {hal-04458310}, eprint = {2402.09814}, archiveprefix = {arXiv}, primaryclass = {math.NA}, keywords = {prex2,nemesis} } @Misc{ Di-Pietro.Hanot.ea:24, author = {Di Pietro, D. A. and Hanot, M.-L. and Salah, M.}, title = {Serendipity discrete complexes with enhanced regularity}, year = {2024}, month = {7}, hal = {hal-04651866}, eprint = {2407.12625}, archiveprefix = {arXiv}, primaryclass = {math.NA}, keywords = {prex2,nemesis} } @Article{ Castanon-Quiroz.Di-Pietro:24, title = {A pressure-robust {HHO} method for the solution of the incompressible {Navier--Stokes} equations on general meshes}, author = {Casta\~{n}\'{o}n Quiroz, D. and Di Pietro, D. A.}, year = {2024}, journal = {IMA J. Numer. Anal.}, doi = {10.1093/imanum/drad007}, volume = {44}, number = {1}, pages = {397--434}, hal = {hal-03608248}, eprint = {2203.07180}, archiveprefix = {arXiv}, primaryclass = {math.NA}, keywords = {prex2,anr-mrsei,rhamnus} } @Misc{ Di-Pietro.Dong.ea:24, title = {Homogeneous multigrid for hybrid discretizations: application to {HHO} methods}, author = {Di Pietro, D. A. and Dong, Z. and Kanschat, G. and Matalon, P. and Rupp, A.}, year = {2024}, month = {3}, hal = {hal-04518103}, eprint = {2403.15858}, archiveprefix = {arXiv}, primaryclass = {math.NA}, keywords = {prex2,nemesis} } @Article{ Fontana.Di-Pietro:24, title = {An a posteriori error analysis based on equilibrated stresses for finite element approximations of frictional contact}, author = {Fontana, I. and Di Pietro, D. A.}, journal = {Comput. Meth. Appl. Mech. Engrg.}, year = {2024}, volume = {425}, number = {116950}, doi = {10.1016/j.cma.2024.116950}, hal = {hal-04375623}, eprint = {2401.02944}, archiveprefix = {arXiv}, primaryclass = {math.NA}, keywords = {prex2,nemesis} } @Article{ Di-Pietro.Droniou.ea:24, title = {A pressure-robust {Discrete de Rham} scheme for the {Navier--Stokes} equations}, author = {Di Pietro, D. A. and Droniou, J. and Qian, J. J.}, journal = {Comput. Meth. Appl. Mech. Engrg.}, year = {2024}, volume = {421}, number = {116765}, doi = {10.1016/j.cma.2024.116765}, hal = {hal-04375767}, eprint = {2401.04456}, archiveprefix = {arXiv}, primaryclass = {math.NA}, keywords = {prex2,nemesis} } @Article{ Di-Pietro:24, title = {An arbitrary-order discrete rot-rot complex on polygonal meshes with application to a quad-rot problem}, author = {Di Pietro, D. A.}, year = {2024}, journal = {IMA J. Numer. Anal.}, volume = {44}, number = {3}, pages = {1699--1730}, doi = {10.1093/imanum/drad045}, hal = {hal-03830503}, eprint = {2210.15581}, archiveprefix = {arXiv}, primaryclass = {math.NA}, keywords = {prex2} } @Article{ Di-Pietro.Droniou.ea:23, title = {Cohomology of the discrete {de Rham} complex on domains of general topology}, author = {Di Pietro, D. A. and Droniou, J. and Pitassi, S.}, year = {2023}, journal = {Calcolo}, doi = {10.1007/s10092-023-00523-7}, volume = {60}, number = {32}, hal = {hal-03767946}, eprint = {2209.00957}, archiveprefix = {arXiv}, primaryclass = {math.NA}, keywords = {prex2} } @Article{ Di-Pietro.Droniou:23, title = {A polytopal method for the {Brinkman} problem robust in all regimes}, author = {Di Pietro, D. A. and Droniou, J.}, journal = {Comput. Meth. Appl. Mech. Engrg.}, year = {2023}, volume = {409}, number = {115981}, doi = {10.1016/j.cma.2023.115981}, hal = {hal-03930849}, eprint = {2301.03272}, archiveprefix = {arXiv}, primaryclass = {math.NA}, keywords = {prex2,anr-mrsei} } @Article{ Di-Pietro.Droniou:23*1, author = {Di Pietro, D. A. and Droniou, J.}, title = {An arbitrary-order discrete {de Rham} complex on polyhedral meshes: Exactness, {Poincar\'e} inequalities, and consistency}, journal = {Found. Comput. Math.}, year = {2023}, volume = {23}, pages = {85--164}, doi = {10.1007/s10208-021-09542-8}, hal = {hal-04536890}, eprint = {2101.04940}, archiveprefix = {arXiv}, primaryclass = {math.NA}, keywords = {prex2} } @Article{ Di-Pietro.Droniou:23*2, title = {Homological- and analytical-preserving serendipity framework for polytopal complexes, with application to the {DDR} method}, author = {Di Pietro, D. A. and Droniou, J.}, journal = {ESAIM: Math. Model Numer. Anal.}, year = {2023}, doi = {10.1051/m2an/2022067}, volume = {57}, number = {1}, pages = {191--225}, hal = {hal-03598859}, eprint = {2203.02939}, archiveprefix = {arXiv}, primaryclass = {math.NA}, keywords = {prex2,anr-mrsei,rhamnus} } @Article{ Di-Pietro.Matalon.ea:23, title = {High-order multigrid strategies for {HHO} discretizations of elliptic equations}, author = {Di Pietro, D. A. and Matalon, P. and Mycek, P. and R\"ude, U.}, journal = {Numer. Linear Algebra with Appl.}, year = {2023}, volume = {30}, number = {e2456}, doi = {10.1002/nla.2456}, hal = {hal-03531293}, keywords = {prex2,fast4hho} } @Article{ Botti.Di-Pietro.ea:23, title = {A serendipity fully discrete div-div complex on polygonal meshes}, author = {Botti, M. and Di Pietro, D. A. and Salah, M.}, year = {2023}, journal = {Comptes Rendus M\'{e}canique}, volume = {351}, number = {S1}, doi = {10.5802/crmeca.150}, hal = {hal-03723495}, eprint = {2207.07194}, archiveprefix = {arXiv}, primaryclass = {math.NA}, keywords = {prex2} } @Article{ Di-Pietro.Droniou:23*3, title = {A fully discrete plates complex on polygonal meshes with application to the {Kirchhoff}--{Love} problem}, author = {Di Pietro, D. A. and Droniou, J.}, journal = {Math. Comp.}, year = {2023}, doi = {10.1090/mcom/3765}, volume = {92}, number = {339}, pages = {51--77}, hal = {hal-03504496}, eprint = {2112.14497}, archiveprefix = {arXiv}, primaryclass = {math.NA}, keywords = {prex2,anr-mrsei,rhamnus} } @Article{ Castanon-Quiroz.Di-Pietro.ea:23, author = {Casta\~{n}\'{o}n Quiroz, D. and Di Pietro, D. A. and Harnist, A.}, title = {A {Hybrid High-Order} method for incompressible flows of non-{Newtonian} fluids with power-like convective behaviour}, year = {2023}, journal = {IMA J. Numer. Anal.}, volume = {43}, number = {1}, pages = {144--186}, doi = {10.1093/imanum/drab087}, hal = {hal-03273118}, primaryclass = {math.NA}, keywords = {prex} } @Article{ Di-Pietro.Hulsemann.ea:23, author = {Di Pietro, D. A. and H\"ulsemann, F. and Matalon, P. and Mycek, P. and R\"ude, U. and Ruiz, D.}, title = {Algebraic multigrid preconditioner for statically condensed systems arising from lowest-order hybrid discretizations}, journal = {SIAM J. Sci. Comput.}, volume = {45}, number = {3}, doi = {10.1137/21M1429849}, year = {2023}, hal = {hal-03272468}, keywords = {fast4hho,prex2} } @Article{ Di-Pietro.Droniou:22, author = {Di Pietro, D. A. and Droniou, J.}, title = {A discrete {de Rham} method for the {Reissner--Mindlin} plate bending problem on polygonal meshes}, year = {2022}, journal = {Comput. Math. Appl.}, volume = {125}, pages = {136--149}, doi = {10.1016/j.camwa.2022.08.041}, hal = {hal-03234088}, eprint = {2105.11773}, archiveprefix = {arXiv}, primaryclass = {math.NA}, keywords = {prex2} } @Article{ Beirao-da-Veiga.Dassi.ea:22, title = {Arbitrary-order pressure-robust {DDR} and {VEM} methods for the {Stokes} problem on polyhedral meshes}, author = {Beir\~{a}o da Veiga, L. and Dassi, F. and Di Pietro, D. A. and Droniou, J.}, year = {2022}, journal = {Comput. Meth. Appl. Mech. Engrg.}, volume = {397}, number = {115061}, hal = {hal-03491878}, doi = {10.1016/j.cma.2022.115061}, url = {https://authors.elsevier.com/a/1fChmAQEIzVqH}, keywords = {prex2,anr-mrsei,rhamnus} } @Article{ Di-Pietro.Fontana.ea:22, author = {Di Pietro, D. A. and Fontana, I. and Kazymyrenko, K.}, title = {A posteriori error estimates via equilibrated stress reconstructions for contact problems approximated by {Nitsche}'s method}, year = {2022}, journal = {Comput. Math. Appl.}, volume = {111}, pages = {61--80}, doi = {10.1016/j.camwa.2022.02.008}, hal = {hal-03354078}, primaryclass = {math.NA}, url = {https://authors.elsevier.com/c/1egEh3CDPQ2-a5}, keywords = {prex2} } @Article{ Chave.Di-Pietro.ea:22, author = {Chave, F. and Di Pietro, D. A. and Lemaire, S.}, title = {A discrete {Weber} inequality on three-dimensional hybrid spaces with application to the {HHO} approximation of magnetostatics}, journal = {Math. Models Methods Appl. Sci.}, year = {2022}, volume = {32}, number = {1}, pages = {175--207}, hal = {hal-02892526}, doi = {10.1142/S0218202522500051}, primaryclass = {math.NA}, keywords = {prex} } @Article{ Botti.Di-Pietro:22, author = {Botti, L. and Di Pietro, D. A.}, title = {$p$-Multilevel preconditioners for HHO discretizations of the {Stokes} equations with static condensation}, year = {2022}, journal = {Commun. Appl. Math. Comput.}, volume = {4}, number = {3}, pages = {783--822}, doi = {10.1007/s42967-021-00142-5}, hal = {hal-02951823}, keywords = {prex} } @Misc{ Fontana.Kazymyrenko.ea:21, title = {Hyperelastic nature of the {Hoek}--{Brown} criterion}, author = {Fontana, I. and Kazymyrenko, K. and Di Pietro, D. A.}, month = {12}, year = {2021}, howpublished = {Submitted}, hal = {hal-03501788}, keywords = {prex2} } @Article{ Botti.Botti.ea:21, author = {Botti, L. and Botti, M. and Di Pietro, D. A.}, title = {An abstract analysis framework for monolithic discretisations of poroelasticity with application to {Hybrid High-Order} methods}, year = {2021}, journal = {Comput. Math. Appl.}, volume = {91}, number = {1}, pages = {150--175}, doi = {10.1016/j.camwa.2020.06.004}, hal = {hal-02398946}, primaryclass = {math.NA}, keywords = {prex} } @InBook{ Botti.Botti.ea:21*1, author = {Botti, L. and Botti, M. and Di Pietro, D. A.}, title = {Polyhedral Methods in Geosciences}, chapter = {A Hybrid High-Order method for multiple-network poroelasticity}, editor = {D. A. Di Pietro, L. Formaggia, R. Masson}, publisher = {Springer}, year = {2021}, number = {27}, series = {SEMA-SIMAI}, isbn = {978-3-030-69362-6}, pages = {227--258}, doi = {10.1007/978-3-030-69363-3_6}, hal = {hal-02461755}, keywords = {prex} } @Article{ Botti.Castanon-Quiroz.ea:21, author = {Botti, M. and Casta\~{n}\'{o}n Quiroz, D. and Di Pietro, D. A. and Harnist, A.}, title = {A {Hybrid High-Order} method for creeping flows of non-{Newtonian} fluids}, journal = {ESAIM: Math. Model Numer. Anal.}, year = {2021}, volume = {55}, number = {5}, pages = {2045--2073}, doi = {10.1051/m2an/2021051}, hal = {hal-02519233}, primaryclass = {math.NA}, keywords = {prex} } @Article{ Di-Pietro.Droniou.ea:21, author = {Di Pietro, D. A. and Droniou, J. and Harnist, A.}, title = {Improved error estimates for {Hybrid High-Order} discretizations of {Leray--Lions} problems}, year = {2021}, journal = {Calcolo}, volume = {58}, number = {19}, doi = {10.1007/s10092-021-00410-z}, hal = {hal-03049154}, primaryclass = {math.NA}, keywords = {prex} } @Article{ Di-Pietro.Droniou:21, author = {Di Pietro, D. A. and Droniou, J.}, title = {An arbitrary-order method for magnetostatics on polyhedral meshes based on a discrete {de Rham} sequence}, year = {2021}, journal = {J. Comput. Phys.}, volume = {429}, number = {109991}, primaryclass = {math.NA}, doi = {10.1016/j.jcp.2020.109991}, hal = {hal-02573274}, keywords = {prex} } @Book{ Di-Pietro.Formaggia.ea:21, editor = {Di Pietro, D. A. and Formaggia, L. and Masson, R.}, title = {Polyhedral Methods in Geosciences}, publisher = {Springer International Publishing}, series = {SEMA-SIMAI}, volume = {27}, isbn = {978-3-030-69362-6}, doi = {10.1007/978-3-030-69363-3}, year = {2021}, image = {polyhedral-methods-geosciences.jpg}, keywords = {edited,HHOMM,prex} } @Article{ Di-Pietro.Hulsemann.ea:21, author = {Di Pietro, D. A. and H\"ulsemann, F. and Matalon, P. and Mycek, P. and R\"ude, U. and Ruiz, D.}, title = {Towards robust, fast solutions of elliptic equations on complex domains through {HHO} discretizations and non-nested multigrid methods}, year = {2021}, journal = {Internat. J. Numer. Methods Engrg.}, volume = {122}, number = {22}, pages = {6576--6595}, hal = {hal-03163476}, doi = {10.1002/nme.6803}, keywords = {prex} } @Article{ Di-Pietro.Hulsemann.ea:21*1, author = {Di Pietro, D. A. and H\"ulsemann, F. and Matalon, P. and Mycek, P. and R\"ude, U. and Ruiz, D.}, title = {An $h$-multigrid method for {Hybrid High-Order} discretizations}, journal = {SIAM J. Sci. Comput.}, doi = {10.1137/20M1342471}, volume = {43}, number = {5}, pages = {S839--S861}, year = {2021}, hal = {hal-02434411}, keywords = {fast4hho,prex} } @Article{ Botti.Di-Pietro.ea:20, author = {Botti, M. and Di Pietro, D. A. and Le Ma\^itre, O. and Sochala, P.}, title = {Numerical approximation of poroelasticity with random coefficients using {Polynomial Chaos} and {Hybrid High-Order} methods}, journal = {Comput. Meth. Appl. Mech. Engrg.}, year = {2020}, volume = {361}, number = {112736}, doi = {10.1016/j.cma.2019.112736}, hal = {hal-02081647}, primaryclass = {math.NA}, keywords = {prex} } @Article{ Botti.Di-Pietro.ea:20*1, author = {Botti, M. and Di Pietro, D. A. and Sochala, P.}, title = {A {Hybrid High-Order} discretisation method for nonlinear poroelasticity}, journal = {Comput. Meth. Appl. Math.}, hal = {hal-01785810}, year = {2020}, volume = {20}, number = {2}, pages = {227--249}, doi = {10.1515/cmam-2018-0142}, primaryclass = {math.NA}, keywords = {prex,HHOMM} } @Article{ Castanon-Quiroz.Di-Pietro:20, author = {Casta\~{n}\'{o}n Quiroz, D. and Di Pietro, D. A.}, title = {A {Hybrid High-Order} method for the incompressible {Navier--Stokes} problem robust for large irrotational body forces}, year = {2020}, volume = {79}, number = {8}, pages = {2655--2677}, journal = {Comput. Math. Appl.}, doi = {10.1016/j.camwa.2019.12.005}, hal = {hal-02151236}, keywords = {HHOMM,prex} } @InProceedings{ Chave.Di-Pietro.ea:20, author = {Chave, F. and Di Pietro, D. A. and Lemaire, S.}, title = {A three-dimensional {Hybrid High-Order} method for magnetostatics}, booktitle = {Finite Volumes for Complex Applications IX -- Methods, Theoretical Aspects, Examples}, editor = {R. Kl\"{o}fkorn and E. Keilegavlen and F. A. Radu and J. Fuhrmann}, year = {2020}, pages = {255--263}, doi = {10.1007/978-3-030-43651-3_22}, hal = {hal-02407175}, keywords = {prex} } @Article{ Di-Pietro.Droniou.ea:20, author = {Di Pietro, D. A. and Droniou, J. and Rapetti, F.}, title = {Fully discrete polynomial {de Rham} sequences of arbitrary degree on polygons and polyhedra}, journal = {Math. Models Methods Appl. Sci.}, year = {2020}, volume = {30}, number = {9}, pages = {1809-1855}, doi = {10.1142/S0218202520500372}, hal = {hal-02356810}, primaryclass = {math.NA}, keywords = {prex} } @Book{ Di-Pietro.Droniou:20, author = {Di Pietro, D. A. and Droniou, J.}, title = {The {Hybrid High-Order} method for polytopal meshes}, subtitle = {Design, analysis, and applications}, publisher = {Springer International Publishing}, year = {2020}, series = {Modeling, Simulation and Application}, volume = {19}, doi = {10.1007/978-3-030-37203-3}, isbn = {978-3-030-37202-6}, hal = {hal-02151813}, image = {hho-book.jpg}, keywords = {research,prex} } @Article{ Botti.Di-Pietro.ea:19, author = {Botti, M. and Di Pietro, D. A. and Guglielmana, A.}, title = {A low-order nonconforming method for linear elasticity on general meshes}, journal = {Comput. Meth. Appl. Mech. Engrg.}, year = {2019}, volume = {354}, pages = {96--118}, doi = {10.1016/j.cma.2019.05.031}, hal = {hal-02009407}, primaryclass = {math.NA}, keywords = {HHOMM,fast4hho,prex} } @Article{ Botti.Di-Pietro.ea:19*1, author = {Botti, L. and Di Pietro, D. A. and Droniou, J.}, title = {A {Hybrid High-Order} method for the incompressible {Navier--Stokes} equations based on {Temam}'s device}, year = {2019}, volume = {376}, pages = {786--816}, doi = {10.1016/j.jcp.2018.10.014}, primaryclass = {math.NA}, hal = {hal-01867134}, journal = {J. Comput. Phys.}, keywords = {HHOMM,fast4hho,prex} } @Article{ Chave.Di-Pietro.ea:19, author = {Chave, F. and Di Pietro, D. A. and Formaggia, L.}, title = {A {Hybrid High-Order} method for passive transport in fractured porous media}, hal = {hal-01784181}, year = {2019}, volume = {10}, number = {12}, journal = {Int. J. Geomath.}, doi = {10.1007/s13137-019-0114-x}, url = {https://rdcu.be/bjHYw}, keywords = {HHOMM,prex} } @Article{ Lelievre.Perotto.ea:19, author = {Leli\`{e}vre, T. and Perotto, S. and Rozza, G. and Di Pietro, D. A. and Ern, A. and Formaggia, L.}, title = {Preface: {S}pecial {I}ssue on {M}odel {R}eduction}, journal = {J. Sci. Comput.}, volume = {81}, issue = {1}, pages = {1--2}, doi = {10.1007/s10915-019-01037-7}, year = {2019}, note = {[Editorial]}, keywords = {prex} } @Article{ Aghili.Di-Pietro:18, author = {Aghili, J. and Di Pietro, D. A.}, title = {An advection-robust {Hybrid High-Order} method for the {Oseen} problem}, year = {2018}, journal = {J. Sci. Comput.}, hal = {hal-01658263}, primaryclass = {math.NA}, volume = {77}, number = {3}, pages = {1310--1338}, doi = {10.1007/s10915-018-0681-2}, keywords = {HHOMM,prex} } @Article{ Boffi.Di-Pietro:18, author = {Boffi, D. and Di Pietro, D. A.}, title = {Unified formulation and analysis of mixed and primal discontinuous skeletal methods on polytopal meshes}, journal = {ESAIM: Math. Model Numer. Anal.}, year = {2018}, volume = {52}, number = {1}, pages = {1--28}, hal = {hal-01365938}, primaryclass = {math.NA}, doi = {10.1051/m2an/2017036}, keywords = {HHOMM,prex} } @Article{ Bonaldi.Di-Pietro.ea:18, author = {Bonaldi, F. and Di Pietro, D. A. and Geymonat, G. and Krasucki, F.}, title = {A {Hybrid High-Order} method for {Kirchhoff--Love} plate bending problems}, journal = {ESAIM: Math. Model Numer. Anal.}, volume = {52}, number = {2}, pages = {393--421}, year = {2018}, hal = {hal-01541389}, primaryclass = {math.NA}, doi = {10.1051/m2an/2017065}, keywords = {HHOMM,prex} } @Article{ Botti.Di-Pietro.ea:18, author = {Botti, L. and Di Pietro, D. A. and Droniou, J.}, title = {A {Hybrid High-Order} discretisation of the {Brinkman} problem robust in the {Darcy} and {Stokes} limits}, journal = {Comput. Meth. Appl. Mech. Engrg.}, hal = {hal-01746367}, year = {2018}, volume = {341}, pages = {278--310}, doi = {10.1016/j.cma.2018.07.004}, primaryclass = {math.NA}, keywords = {HHOMM,prex} } @Article{ Botti.Di-Pietro:18, author = {Botti, L. and Di Pietro, D. A.}, title = {Assessment of {Hybrid High-Order} methods on curved meshes and comparison with discontinuous {Galerkin} methods}, journal = {J. Comput. Phys.}, year = {2018}, hal = {hal-01581883}, volume = {370}, pages = {58--84}, doi = {10.1016/j.jcp.2018.05.017}, keywords = {HHOMM,prex} } @Article{ Chave.Di-Pietro.ea:18, author = {Chave, F. and Di Pietro, D. A. and Formaggia, L.}, title = {A {Hybrid High-Order} method for {Darcy} flows in fractured porous media}, year = {2018}, journal = {SIAM J. Sci. Comput.}, volume = {40}, number = {2}, pages = {A1063--A1094}, doi = {10.1137/17M1119500}, hal = {hal-01482925}, keywords = {HHOMM,prex} } @Article{ Cicuttin.Di-Pietro.ea:18, author = {Cicuttin, M. and Di Pietro, D. A. and Ern, A.}, title = {Implementation of {Discontinuous Skeletal} methods on arbitrary-dimensional, polytopal meshes using generic programming}, journal = {J. Comput. Appl. Math.}, volume = {344}, pages = {852--874}, year = {2018}, hal = {hal-01429292}, keywords = {HHOMM,prex}, doi = {10.1016/j.cam.2017.09.017} } @Article{ Di-Pietro.Droniou.ea:18, author = {Di Pietro, D. A. and Droniou, J. and Manzini, G.}, title = {{Discontinuous Skeletal Gradient Discretisation} methods on polytopal meshes}, journal = {J. Comput. Phys.}, year = {2018}, volume = {355}, pages = {397--425}, hal = {hal-01564598}, primaryclass = {math.NA}, doi = {10.1016/j.jcp.2017.11.018}, keywords = {HHOMM,prex} } @Article{ Di-Pietro.Droniou:18, author = {Di Pietro, D. A. and Droniou, J.}, title = {A third {Strang} lemma and an {Aubin}--{Nitsche} trick for schemes in fully discrete formulation}, hal = {hal-01778044}, primaryclass = {math.NA}, year = {2018}, journal = {Calcolo}, volume = {55}, number = {40}, doi = {10.1007/s10092-018-0282-3}, url = {https://rdcu.be/5L8F}, keywords = {HHOMM,prex} } @Book{ Di-Pietro.Ern.ea:18, editor = {Di Pietro, D. A. and Ern, A. and Formaggia, L.}, title = {Numerical Methods for PDEs}, subtitle = {State of the Art Techniques}, publisher = {Springer International Publishing}, series = {SEMA-SIMAI}, volume = {15}, doi = {10.1007/978-3-319-94676-4}, isbn = {978-3-319-94675-7}, year = {2018}, hal = {hal-01818426}, image = {ihp-book.jpg}, keywords = {edited,HHOMM,prex} } @InBook{ Di-Pietro.Ern.ea:18*1, author = {Di Pietro, D. A. and Ern, A. and Formaggia, L.}, title = {Numerical Methods for PDEs}, subtitle = {State of the Art Techniques}, chapter = {An introduction to recent developments in numerical methods for partial differential equations}, editor = {D. A. Di Pietro, A. Ern, L. Formaggia}, publisher = {Springer}, year = {2018}, number = {15}, series = {SEMA-SIMAI}, isbn = {978-3-319-94675-7}, hal = {hal-01490524}, primaryclass = {math.NA}, doi = {10.1007/978-3-319-94676-4_1}, pages = {1--4}, keywords = {HHOMM,prex} } @Article{ Di-Pietro.Krell:18, author = {Di Pietro, D. A. and Krell, S.}, title = {A {Hybrid High-Order} method for the steady incompressible {Navier--Stokes} problem}, journal = {J. Sci. Comput.}, year = {2018}, volume = {74}, number = {3}, pages = {1677--1705}, hal = {hal-01349519}, primaryclass = {math.NA}, doi = {10.1007/s10915-017-0512-x}, keywords = {HHOMM,prex} } @Article{ Di-Pietro.Marche:18, author = {Di Pietro, D. A. and Marche, F.}, title = {{Weighted Interior Penalty} discretization of fully nonlinear and weakly dispersive free surface shallow water flows}, journal = {J. Comput. Phys.}, volume = {355}, pages = {285--309}, year = {2018}, hal = {hal-01566446}, keywords = {HHOMM,prex}, doi = {10.1016/j.jcp.2017.11.009} } @InBook{ Di-Pietro.Tittarelli:18, author = {Di Pietro, D. A. and Tittarelli, R.}, title = {Numerical Methods for PDEs}, subtitle = {State of the Art Techniques}, chapter = {An introduction to Hybrid High-Order methods}, editor = {D. A. Di Pietro, A. Ern, L. Formaggia}, publisher = {Springer}, year = {2018}, pages = {75--128}, number = {15}, series = {SEMA-SIMAI}, isbn = {978-3-319-94675-7}, hal = {hal-01490524}, primaryclass = {math.NA}, doi = {10.1007/978-3-319-94676-4_4}, keywords = {HHOMM,prex} } @Article{ Aghili.Di-Pietro.ea:17, author = {Aghili, J. and Di Pietro, D. A. and Ruffini, B.}, title = {An $hp$-{Hybrid High-Order} method for variable diffusion on general meshes}, journal = {Comput. Meth. Appl. Math.}, year = {2017}, volume = {17}, number = {3}, pages = {359--376}, doi = {10.1515/cmam-2017-0009}, hal = {hal-01290251}, keywords = {HHOMM,prex} } @Article{ Botti.Di-Pietro.ea:17, author = {Botti, M. and Di Pietro, D. A. and Sochala, P.}, title = {A {Hybrid High-Order} method for nonlinear elasticity}, year = {2017}, journal = {SIAM J. Numer. Anal.}, volume = {55}, number = {6}, pages = {2687--2717}, doi = {10.1137/16M1105943}, hal = {hal-01539510}, primaryclass = {math.NA}, keywords = {HHOMM,prex} } @InProceedings{ Botti.Di-Pietro.ea:17*1, author = {Botti, M. and Di Pietro, D. A. and Sochala, P.}, title = {A nonconforming high-order method for nonlinear poroelasticity}, booktitle = {Finite Volumes for Complex Applications VIII -- Hyperbolic, Elliptic and Parabolic Problems}, editor = {C. Canc\`{e}s and P. Omnes}, year = {2017}, pages = {537--546}, doi = {10.1007/978-3-319-57397-7}, hal = {hal-01439165}, keywords = {HHOMM,prex} } @InProceedings{ Chave.Di-Pietro.ea:17, author = {Chave, F. and Di Pietro, D. A. and Marche, F.}, title = {A {Hybrid High-Order} method for the convective {Cahn--Hilliard} problem in mixed form}, booktitle = {Finite Volumes for Complex Applications VIII -- Hyperbolic, Elliptic and Parabolic Problems}, editor = {C. Canc\`{e}s and P. Omnes}, year = {2017}, pages = {517--526}, doi = {10.1007/978-3-319-57397-7}, keywords = {HHOMM,prex}, hal = {hal-01477247}, primaryclass = {math.NA} } @Article{ Di-Pietro.Droniou:17, author = {Di Pietro, D. A. and Droniou, J.}, title = {{$W^{s,p}$}-approximation properties of elliptic projectors on polynomial spaces, with application to the error analysis of a {Hybrid High-Order} discretisation of {Leray--Lions} problems}, journal = {Math. Models Methods Appl. Sci.}, year = {2017}, volume = {27}, number = {5}, pages = {879--908}, doi = {10.1142/S0218202517500191}, hal = {hal-01326818}, primaryclass = {math.NA}, keywords = {HHOMM,prex} } @Article{ Di-Pietro.Droniou:17*1, author = {Di Pietro, D. A. and Droniou, J.}, title = {A {Hybrid High-Order} method for {Leray--Lions} elliptic equations on general meshes}, journal = {Math. Comp.}, year = {2017}, volume = {86}, number = {307}, pages = {2159--2191}, doi = {10.1090/mcom/3180}, hal = {hal-01183484}, primaryclass = {math.NA}, keywords = {HHOMM,prex} } @Article{ Di-Pietro.Ern:17, author = {Di Pietro, D. A. and Ern, A.}, title = {Arbitrary-order mixed methods for heterogeneous anisotropic diffusion on general meshes}, journal = {IMA J. Numer. Anal.}, year = {2017}, volume = {37}, number = {1}, pages = {40--63}, doi = {10.1093/imanum/drw003}, hal = {hal-00918482}, keywords = {HHOMM,prex} } @Article{ Di-Pietro.Kapidani.ea:17, author = {Di Pietro, D. A. and Kapidani, B. and Specogna, R. and Trevisan, F.}, title = {An arbitrary-order discontinuous skeletal method for solving electrostatics on general polyhedral meshes}, journal = {IEEE Transactions on Magnetics}, year = {2017}, volume = {53}, number = {6}, pages = {1--4}, doi = {10.1109/TMAG.2017.2666546}, hal = {hal-01399505}, keywords = {HHOMM,prex} } @InProceedings{ Di-Pietro.Krell:17, author = {Di Pietro, D. A. and Krell, S.}, title = {Benchmark session: {T}he {2D} {Hybrid High-Order} method}, booktitle = {Finite Volumes for Complex Applications VIII -- Methods and Theoretical Aspects}, editor = {C. Canc\`{e}s and P. Omnes}, year = {2017}, pages = {91--106}, doi = {10.1007/978-3-319-57397-7}, keywords = {HHOMM,prex}, hal = {hal-01818217} } @Article{ Riedlbeck.Di-Pietro.ea:17, author = {Riedlbeck, R. and Di Pietro, D. A. and Ern, A. and Granet, S. and Kazymyrenko, K.}, title = {Stress and flux reconstruction in Biot's poro-elasticity problem with application to a posteriori error analysis}, year = {2017}, journal = {Comput. Math. Appl.}, volume = {73}, number = {7}, pages = {1593--1610}, doi = {10.1016/j.camwa.2017.02.005}, hal = {hal-01366646}, keywords = {HHOMM,prex} } @InProceedings{ Riedlbeck.Di-Pietro.ea:17*1, author = {Riedlbeck, R. and Di Pietro, D. A. and Ern, A.}, title = {Equilibrated stress reconstruction for linear elasticity problems with application to a posteriori error analysis}, booktitle = {Finite Volumes for Complex Applications VIII -- Methods and Theoretical Aspects}, editor = {C. Canc\`{e}s and P. Omnes}, year = {2017}, pages = {293--302}, hal = {hal-01433841}, keywords = {HHOMM,prex} } @Article{ Boffi.Botti.ea:16, author = {Boffi, D. and Botti, M. and Di Pietro, D. A.}, title = {A nonconforming high-order method for the {Biot} problem on general meshes}, journal = {SIAM J. Sci. Comput.}, year = {2016}, volume = {38}, number = {3}, pages = {A1508--A1537}, doi = {10.1137/15M1025505}, hal = {hal-01162976}, primaryclass = {math.NA}, keywords = {HHOMM} } @Article{ Chave.Di-Pietro.ea:16, author = {Chave, F. and Di Pietro, D. A. and Marche, F. and Pigeonneau, F.}, title = {A Hybrid High-Order method for the {Cahn--Hilliard} problem in mixed form}, journal = {SIAM J. Numer. Anal.}, year = {2016}, volume = {54}, number = {3}, pages = {1873--1898}, hal = {hal-01203733}, primaryclass = {math.NA}, doi = {10.1137/15M1041055}, keywords = {HHOMM} } @Article{ Cockburn.Di-Pietro.ea:16, title = {Bridging the {Hybrid High-Order} and {Hybridizable Discontinuous Galerkin} methods}, author = {Cockburn, B. and Di Pietro, D. A. and Ern, A.}, journal = {ESAIM: Math. Model Numer. Anal.}, year = {2016}, volume = {50}, number = {3}, pages = {635--650}, hal = {hal-01115318}, doi = {10.1051/m2an/2015051} } @Article{ Di-Pietro.Ern.ea:16, author = {Di Pietro, D. A. and Ern, A. and Linke, A. and Schieweck, F.}, title = {A discontinuous skeletal method for the viscosity-dependent {Stokes} problem}, journal = {Comput. Meth. Appl. Mech. Engrg.}, year = {2016}, volume = {306}, pages = {175--195}, hal = {hal-01244387}, keywords = {HHOMM}, doi = {10.1016/j.cma.2016.03.033} } @InBook{ Di-Pietro.Ern.ea:16*1, author = {Di Pietro, D. A. and Ern, A. and Lemaire, S.}, title = {Building bridges: Connections and challenges in modern approaches to numerical partial differential equations}, chapter = {A review of Hybrid High-Order methods: formulations, computational aspects, comparison with other methods}, editor = {Barrenechea, G. and Brezzi, F. and Cangiani, A. and Georgoulis, M.}, publisher = {Springer}, year = {2016}, pages = {205--236}, hal = {hal-01163569}, isbn = {978-3-319-41638-0}, doi = {10.1007/978-3-319-41640-3}, keywords = {HHOMM} } @Article{ Di-Pietro.Specogna:16, author = {Di Pietro, D. A. and Specogna, R.}, title = {An a posteriori-driven adaptive {Mixed High-Order} method with application to electrostatics}, journal = {J. Comput. Phys.}, year = {2016}, volume = {326}, number = {1}, pages = {35--55}, doi = {10.1016/j.jcp.2016.08.041}, hal = {hal-01310313}, keywords = {HHOMM} } @Article{ Aghili.Boyaval.ea:15, author = {Aghili, J. and Boyaval, S. and Di Pietro, D. A.}, title = {Hybridization of mixed high-order methods on general meshes and application to the {Stokes} equations}, journal = {Comput. Meth. Appl. Math.}, year = {2015}, volume = {15}, number = {2}, pages = {111--134}, hal = {hal-01009723}, doi = {10.1515/cmam-2015-0004} } @Article{ Bonelle.Di-Pietro.ea:15, author = {Bonelle, J. and Di Pietro, D. A. and Ern, A.}, title = {Low-order reconstruction operators on polyhedral meshes: Application to {Compatible Discrete Operator} schemes}, journal = {Computer Aided Geometric Design}, year = {2015}, volume = {35--36}, pages = {27--41}, hal = {hal-01097311}, doi = {10.1016/j.cagd.2015.03.015} } @Article{ Di-Pietro.Droniou.ea:15, author = {Di Pietro, D. A. and J. Droniou and Ern, A.}, title = {A discontinuous-skeletal method for advection-diffusion-reaction on general meshes}, year = {2015}, journal = {SIAM J. Numer. Anal.}, volume = {53}, number = {5}, pages = {2135--2157}, hal = {hal-01079342}, primaryclass = {math.NA}, doi = {10.1137/140993971} } @Article{ Di-Pietro.Ern:15, author = {Di Pietro, D. A. and Ern, A.}, title = {Equilibrated tractions for the {Hybrid High-Order} method}, year = {2015}, journal = {C. R. Acad. Sci. Paris, Ser. I}, volume = {353}, pages = {279--282}, hal = {hal-01079026}, primaryclass = {math.NA}, doi = {10.1016/j.crma.2014.12.009} } @Article{ Di-Pietro.Ern:15*1, author = {Di Pietro, D. A. and Ern, A.}, title = {Hybrid high-order methods for variable-diffusion problems on general meshes}, journal = {C. R. Acad. Sci. Paris, Ser. I}, year = {2015}, volume = {353}, pages = {31--34}, doi = {10.1016/j.crma.2014.10.013}, hal = {hal-01023302} } @Article{ Di-Pietro.Ern:15*2, author = {Di Pietro, D. A. and Ern, A.}, title = {A hybrid high-order locking-free method for linear elasticity on general meshes}, journal = {Comput. Meth. Appl. Mech. Engrg.}, year = {2015}, volume = {283}, pages = {1--21}, doi = {10.1016/j.cma.2014.09.009}, hal = {hal-00979435} } @Article{ Di-Pietro.Lemaire:15, title = {An extension of the {Crouzeix--Raviart} space to general meshes with application to quasi-incompressible linear elasticity and {Stokes} flow}, author = {Di Pietro, D. A. and Lemaire, S.}, journal = {Math. Comp.}, year = {2015}, volume = {84}, number = {291}, pages = {1--31}, doi = {10.1090/S0025-5718-2014-02861-5}, hal = {hal-00753660} } @Article{ Di-Pietro.Vohralik.ea:15, title = {Adaptive regularization, linearization, discretization, and a posteriori error control for the two-phase Stefan problem}, author = {Di Pietro, D. A. and Vohral\'{i}k, M. and Yousef, S.}, journal = {Math. Comp.}, year = {2015}, volume = {84}, number = {291}, pages = {153--186}, doi = {10.1090/S0025-5718-2014-02854-8}, hal = {hal-00690862} } @Article{ Di-Pietro.Ern.ea:14, author = {Di Pietro, D. A. and Ern, A. and Lemaire, S.}, title = {An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators}, journal = {Comput. Meth. Appl. Math.}, year = {2014}, volume = {14}, number = {4}, pages = {461--472}, doi = {10.1515/cmam-2014-0018}, note = {Open access (editor's choice)}, hal = {hal-00978198} } @Article{ Di-Pietro.Flauraud.ea:14, author = {Di Pietro, D. A. and Flauraud, E. and Vohral\'{i}k, M. and Yousef, S.}, title = {A posteriori error estimates, stopping criteria, and adaptivity for multiphase compositional Darcy flows in porous media}, journal = {J. Comput. Phys.}, year = {2014}, volume = {274}, pages = {163--187}, doi = {10.1016/j.jcp.2014.06.061}, hal = {hal-00839487} } @Article{ Di-Pietro.Vohralik.ea:14, author = {Di Pietro, D. A. and Vohral\'{i}k, M. and Yousef, S.}, title = {An a posteriori-based, fully adaptive algorithm for thermal multiphase compositional flows in porous media with adaptive mesh refinement}, journal = {Comput. Math. Appl.}, year = {2014}, doi = {10.1016/j.camwa.2014.08.008}, volume = {68}, number = {12}, pages = {2331--2347}, hal = {hal-00856437} } @Article{ Di-Pietro.Vohralik:14, title = {A review of recent advances in discretization methods, a posteriori error analysis, and adaptive algorithms for numerical modeling in geosciences}, author = {Di Pietro, D. A. and Vohral\'{i}k, M.}, journal = {Oil \& Gas Science and Technology}, volume = {69}, number = {4}, pages = {701--730}, year = {2014}, doi = {10.2516/ogst/2013158}, hal = {hal-00783068} } @Article{ Di-Pietro.Gratien.ea:13, author = {Di Pietro, D. A. and Gratien, J.-M. and Prud'homme, C.}, title = {A domain-specific embedded language in {C++} for lowest-order discretizations of diffusive problems on general meshes}, journal = {BIT Numerical Mathematics}, volume = {53}, number = {1}, year = {2013}, pages = {111--152}, doi = {10.1007/s10543-012-0403-3}, hal = {hal-00654406} } @Article{ Di-Pietro.Nicaise:13, author = {Di Pietro, D. A. and Nicaise, S.}, title = {A locking-free discontinuous {G}alerkin method for linear elasticity in locally nearly incompressible heterogeneous media}, journal = {App. Num. Math.}, volume = {63}, year = {2013}, pages = {105--116}, doi = {10.1016/j.apnum.2012.09.009}, hal = {hal-00685020} } @Article{ Di-Pietro:13, author = {Di Pietro, D. A.}, title = {On the conservativity of cell centered {Galerkin} methods}, journal = {C. R. Acad. Sci. Paris, Ser. I}, volume = {351}, number = {3--4}, pages = {155--159}, year = {2013}, doi = {10.1016/j.crma.2013.03.001}, hal = {hal-00781510} } @Article{ Bassi.Botti.ea:12, author = {Bassi, F. and Botti, L. and Colombo, A. and Di Pietro, D. A. and Tesini, P.}, title = {On the flexibility of agglomeration based physical space discontinuous {Galerkin} discretizations}, journal = {J. Comput. Phys.}, volume = {231}, number = {1}, pages = {45--65}, year = {2012}, doi = {10.1016/j.jcp.2011.08.018}, hal = {hal-00562219} } @Book{ Di-Pietro.Ern:12, author = {Di Pietro, D. A. and Ern, A.}, title = {Mathematical aspects of discontinuous {G}alerkin methods}, series = {Math\'ematiques \& Applications (Berlin) [Mathematics \& Applications]}, volume = {69}, publisher = {Springer, Heidelberg}, isbn = {978-3-642-22979-4}, year = {2012}, keywords = {research}, doi = {10.1007/978-3-642-22980-0}, image = {dg-book.jpg}, hal = {hal-01820185} } @Article{ Di-Pietro.Ern:12*1, author = {Di Pietro, D. A. and Ern, A.}, title = {Analysis of a discontinuous {Galerkin} method for heterogeneous diffusion problems with low-regularity solutions}, journal = {Numer. Meth. for PDEs}, year = {2012}, volume = {28}, number = {4}, pages = {1161--1177}, doi = {10.1002/num.20675}, hal = {hal-00514387} } @Article{ Di-Pietro:12, author = {Di Pietro, D. A.}, title = {Cell centered {Galerkin} methods for diffusive problems}, journal = {ESAIM: Math. Model Numer. Anal.}, volume = {46}, number = {1}, year = {2012}, pages = {111--144}, doi = {10.1051/m2an/2011016}, hal = {hal-00511125} } @Article{ Botti.Di-Pietro:11, author = {Botti, L. and Di Pietro, D. A.}, title = {A pressure-correction scheme for convection-dominated incompressible flows with discontinuous velocity and continuous pressure}, journal = {J. Comput. Phys.}, volume = {230}, number = {3}, pages = {572--585}, doi = {10.1016/j.jcp.2010.10.004}, hal = {hal-00458293}, year = {2011} } @InProceedings{ Di-Pietro.Eymard.ea:11, author = {Di Pietro, D. A. and Eymard, R. and Lemaire, S. and Masson, R.}, title = {Hybrid finite volume discretization of linear elasticity models on general meshes}, booktitle = {Finite Volumes for Complex Applications VI}, publisher = {Springer--Verlag}, editor = {Fo\v{r}t, J. and F\"{u}rst, J. and Halama, J. and Herbin, R. and Hubert, F.}, pages = {331--339}, year = {2011}, doi = {10.1007/978-3-642-20671-9_35}, hal = {hal-00795201} } @InProceedings{ Di-Pietro.Gratien:11, author = {Di Pietro, D. A. and Gratien, J.-M.}, title = {Lowest order methods for diffusive problems on general meshes: {A} unified approach to definition and implementation}, booktitle = {Finite Volumes for Complex Applications VI}, publisher = {Springer--Verlag}, editor = {Fo\v{r}t, J. and F\"{u}rst, J. and Halama, J. and Herbin, R. and Hubert, F.}, year = {2011}, pages = {3--19}, note = {Invited paper}, doi = {10.1007/978-3-642-20671-9_84}, hal = {hal-00562500} } @InProceedings{ Di-Pietro.Vohralik.ea:11, author = {Di Pietro, D. A. and Vohral\'{i}k, M. and Widmer, C.}, title = {An a posteriori error estimator for a finite volume discretization of two-phase flow}, booktitle = {Finite Volumes for Complex Applications VI}, publisher = {Springer--Verlag}, editor = {Fo\v{r}t, J. and F\"{u}rst, J. and Halama, J. and Herbin, R. and Hubert, F.}, pages = {341--349}, year = {2011}, doi = {10.1007/978-3-642-20671-9_36} } @Article{ Di-Pietro:11, author = {Di Pietro, D. A.}, title = {A compact cell-centered {Galerkin} method with subgrid stabilization}, journal = {C. R. Acad. Sci. Paris, Ser. I}, volume = {349}, number = {1--2}, year = {2011}, pages = {93--98}, doi = {10.1016/j.crma.2010.11.017}, hal = {hal-00476222} } @Article{ Agelas.Di-Pietro.ea:10, author = {Ag\'{e}las, L. and Di Pietro, D. A. and Droniou, J.}, title = {The {G} method for heterogeneous anisotropic diffusion on general meshes}, journal = {ESAIM: Math. Model Numer. Anal.}, volume = {44}, number = {4}, pages = {597--625}, year = {2010}, doi = {10.1051/m2an/2010021}, hal = {hal-00342739} } @Article{ Agelas.Di-Pietro.ea:10*1, author = {Ag\'{e}las, L. and Di Pietro, D. A. and Eymard, R. and Masson, R.}, title = {An abstract analysis framework for nonconforming approximations of diffusion problems on general meshes}, journal = {IJFV International Journal on Finite Volumes}, volume = {7}, number = {1}, pages = {1--29}, year = {2010}, hal = {hal-00318390} } @Article{ Di-Pietro.Ern:10, author = {Di Pietro, D. A. and Ern, A.}, title = {Discrete functional analysis tools for discontinuous {G}alerkin methods with application to the incompressible {N}avier--{S}tokes equations}, journal = {Math. Comp.}, volume = {79}, year = {2010}, pages = {1303--1330}, doi = {10.1090/S0025-5718-10-02333-1}, hal = {hal-00278925} } @Article{ Di-Pietro:10, author = {Di Pietro, D. A.}, title = {Cell centered {Galerkin} methods}, journal = {C. R. Acad. Sci. Paris, Ser. I}, year = {2010}, volume = {348}, number = {1--2}, pages = {31--34}, doi = {10.1016/j.crma.2009.11.012}, hal = {hal-00398782} } @Thesis{ Di-Pietro:10*1, author = {Di Pietro, D. A.}, title = {M\'{e}thodes non conformes pour des \'{e}quations aux d\'{e}riv\'{e}es partielles avec diffusion}, note = {Habilitation thesis}, school = {Universit\'{e} de Paris-Est}, year = {2010}, url = {http://tel.archives-ouvertes.fr/tel-00550230} } @InProceedings{ Agelas.Di-Pietro.ea:09, author = {Ag\'{e}las, L. and Di Pietro, D. A. and Kapyrin, I.}, title = {A comparison of last generation cell centered finite volume methods on challenging three dimensional problems}, booktitle = {Proceedings of the 3rd International Conference on Approximation Methods and numerical Modeling in Environment and Natural Resources}, address = {Pau, France}, month = {6}, year = {2009} } @Article{ Di-Pietro.Veneziani:09, author = {Di Pietro, D. A. and Veneziani, A.}, title = {Expression template implementation of continuous and discontinuous {G}alerkin methods}, journal = {Comp. Vis. in Sci.}, volume = {12}, year = {2009}, pages = {421--436}, doi = {10.1007/s00791-008-0117-x}, hal = {hal-01818198} } @InProceedings{ Agelas.Di-Pietro.ea:08, author = {Ag\'{e}las, L. and Di Pietro, D. A. and Kapyrin, I. and Masson, R.}, title = {Generalized {L-scheme} for the discretization of diffusion fluxes on general meshes}, booktitle = {Proceedings of the 11th European Conference on the Mathematics of Oil Recovery}, address = {Bergen, Norway}, month = {9}, year = {2008} } @InProceedings{ Agelas.Di-Pietro.ea:08*1, author = {Ag\'{e}las, L. and Di Pietro, D. A. and Eymard, R. and Masson, R.}, title = {A general framework for non-conforming approximations of the single phase {D}arcy equation}, booktitle = {Proceedings of the 11th European Conference on the Mathematics of Oil Recovery}, address = {Bergen, Norway}, month = {9}, year = {2008} } @InProceedings{ Agelas.Di-Pietro.ea:08*2, author = {Ag\'{e}las, L. and Di Pietro, D. A. and Kapyrin, I. and Masson, R.}, title = {The {MPFA G} scheme for heterogeneous anisotropic diffusion problems on general meshes}, booktitle = {Proceedings of the 11th European Conference on the Mathematics of Oil Recovery}, address = {Bergen, Norway}, month = {9}, year = {2008} } @InProceedings{ Agelas.Di-Pietro.ea:08*3, author = {Ag\'{e}las, L. and Di Pietro, D. A. and Masson, R.}, title = {A symmetric and coercive finite volume scheme for multiphase porous media flow with applications in the oil industry}, booktitle = {Finite Volumes for Complex Applications V}, publisher = {John Wiley \& Sons}, editor = {R. Eymard and J.-M. H\'erard}, isbn = {978-1-84821-035-6}, pages = {35--52}, year = {2008}, note = {Invited paper}, hal = {hal-01818220} } @InProceedings{ Agelas.Di-Pietro:08, author = {Ag\'{e}las, L. and Di Pietro, D. A.}, title = {A symmetric finite volume scheme for anisotropic heterogeneous second-order elliptic problems}, booktitle = {Finite Volumes for Complex Applications V}, publisher = {John Wiley \& Sons}, editor = {R. Eymard and J.-M. H\'erard}, isbn = {978-1-84821-035-6}, pages = {705--716}, year = {2008} } @Article{ Di-Pietro.Ern.ea:08, author = {Di Pietro, D. A. and Ern, A. and Guermond, J.-L.}, title = {Discontinuous {G}alerkin methods for anisotropic semi-definite diffusion with advection}, journal = {SIAM J. Numer. Anal.}, volume = {46}, number = {2}, pages = {805--831}, year = {2008}, doi = {10.1137/060676106}, hal = {hal-01818201} } @InProceedings{ Di-Pietro.Ern:08, author = {Di Pietro, D. A. and Ern, A.}, title = {A discontinuous {Galerkin} flux for anisotropic heterogeneous second-order elliptic problems}, booktitle = {Finite Volumes for Complex Applications V}, publisher = {John Wiley \& Sons}, editor = {R. Eymard and J.-M. H\'erard}, isbn = {978-1-84821-035-6}, pages = {777--793}, year = {2008}, hal = {hal-01818221} } @InProceedings{ Mundal.Di-Pietro.ea:08, author = {Mundal, S. and Di Pietro, D. A. and Aavatsmark, I.}, title = {Compact-stencil {MPFA} method for heterogeneous highly-anisotropic second order elliptic problems}, booktitle = {Finite Volumes for Complex Applications V}, publisher = {John Wiley \& Sons}, editor = {R. Eymard and J.-M. H\'erard}, isbn = {978-1-84821-035-6}, pages = {905--918}, year = {2008}, hal = {hal-01818222} } @Article{ Bassi.Crivellini.ea:07, author = {Bassi, F. and Crivellini, A. and Di Pietro, D. A. and Rebay, S.}, title = {An implicit high-order discontinuous {G}alerkin method for steady and unsteady incompressible flows}, year = {2007}, journal = {Comp. \& Fl.}, volume = {36}, number = {10}, pages = {1529--1546}, doi = {10.1016/j.compfluid.2007.03.012}, hal = {hal-01818204} } @Article{ Di-Pietro:07, author = {Di Pietro, D. A.}, title = {Analysis of a discontinuous {G}alerkin approximation of the {S}tokes problem based on an artificial compressibility flux}, year = {2007}, journal = {Int. J. Num. Meth. Fluids}, volume = {55}, number = {8}, pages = {793--813}, doi = {10.1002/fld.1495}, hal = {hal-01818207} } @Article{ Bassi.Crivellini.ea:06, author = {Bassi, F. and Crivellini, A. and Di Pietro, D. A. and Rebay, S.}, title = {An artificial compressibility flux for the discontinuous {Galerkin} solution of the incompressible {Navier-Stokes} equations}, journal = {J. Comput. Phys.}, volume = {218}, number = {2}, year = {2006}, pages = {794--815}, doi = {10.1016/j.jcp.2006.03.006}, hal = {hal-01818209} } @InProceedings{ Bassi.Crivellini.ea:06*1, author = {Bassi, F. and Crivellini, A. and Di Pietro, D. A. and Rebay, S.}, title = {{A high-order discontinuous Galerkin solver for 3D aerodynamic turbulent flows}}, booktitle = {ECCOMAS CFD 2006 Proceedings (Egmond an Zee, Netherlands)}, editor = {P. Wesseling and E. {O\~nate} and J. P\'eriaux}, year = {2006}, month = {9} } @Article{ Di-Pietro.Lo-Forte.ea:06, author = {Di Pietro, D. A. and Lo Forte, S. and Parolini, N.}, title = {Mass preserving finite element implementations of the level set method}, journal = {App. Num. Math.}, volume = {56}, issue = {9}, pages = {1179--1195}, year = {2006}, doi = {10.1016/j.apnum.2006.03.003}, hal = {hal-01818211} } @Thesis{ Di-Pietro:06, author = {Di Pietro, D. A.}, title = {Discontinuous {Galerkin} methods for the incompressible {Navier--Stokes} equations}, school = {Universit\`{a} di Bergamo}, month = {3}, type = {Ph.D. thesis}, year = {2006} } @Article{ Cossali.Di-Pietro.ea:03, author = {Cossali, G. E. and Di Pietro, D. A. and Marengo, M.}, title = {Comparison of four analytical and numerical models for a microchannel heat sink}, journal = {Int. J. Heat and Tech.}, volume = {21}, number = {2}, pages = {31--42}, year = {2003}, hal = {hal-01820286} } @InProceedings{ Cossali.Di-Pietro.ea:03*1, author = {Cossali, G. E. and Di Pietro, D. A. and Marengo, M.}, title = {{Analytical and numerical modeling of microchannel heat sinks}}, booktitle = {Proceedings of the First International Conference on Microchannels and Minichannels (Rochester, New York)}, month = {4}, year = {2003} } @InProceedings{ Cossali.Di-Pietro.ea:02, author = {Cossali, G. E. and Di Pietro, D. A. and Marengo, M.}, title = {{Design of a microchannel cooling system for BTeV particle detector}}, booktitle = {Proceedings of the 8th International Workshop on Thermal Investigations of ICs and Systems (Madrid, Spain)}, month = {9}, year = {2002} }