@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}
}