Daniele A. Di Pietro

Research monographs (2)

	1) D. A. Di Pietro and J. Droniou The Hybrid High-Order Method for Polytopal Meshes Design, Analysis, and Applications Number 19 in Modeling, Simulation and Applications Springer International Publishing, 2020 ISBN 978-3-030-37202-6 (Hardcover) 978-3-030-37203-3 (eBook) DOI: 10.1007/978-3-030-37203-3 HAL preprint hal-02151813
	2) D. A. Di Pietro and A. Ern Mathematical Aspects of Discontinuous Galerkin Methods Number 69 in Mathematics & Applications Springer-Verlag, Berlin, 2012 ISBN 978-3-642-22979-4 (Softcover) 978-3-642-22980-0 (eBook) DOI: 10.1007/978-3-642-22980-0 HAL preprint hal-01820185

Edited monographs (2)

	1) D. A. Di Pietro, L. Formaggia, and R. Masson (Eds.) Polyhedral Methods in Geosciences SEMA-SIMAI Springer International Publishing, 2021 ISBN: 978-3-030-69362-6 DOI: 10.1007/978-3-030-69363-3
	2) D. A. Di Pietro, A. Ern, and L. Formaggia (Eds.) Numerical Methods for PDEs: State of the Art Techniques Number 15 in SEMA-SIMAI Springer International Publishing, 2018 ISBN 978-3-319-94675-7 (Hardcover) 978-3-319-94676-4 (eBook) DOI: 10.1007/978-3-319-94676-4 HAL preprint hal-01818426

Papers (84)

1) D. A. Di Pietro
An arbitrary-order discrete rot-rot complex on polygonal meshes with application to a quad-rot problem
IMA J. Numer. Anal., 2023. Accepted for publication
HAL preprint hal-03830503, arXiv preprint 2210.15581 [math.NA]

2) D. A. Di Pietro, J. Droniou, and S. Pitassi
Cohomology of the discrete de Rham complex on domains of general topology
Calcolo, 2023, 60(32). DOI: 10.1007/s10092-023-00523-7
HAL preprint hal-03767946, arXiv preprint 2209.00957 [math.NA]

3) D. A. Di Pietro and J. Droniou
A polytopal method for the Brinkman problem robust in all regimes
Comput. Meth. Appl. Mech. Engrg., 2023, 409(115981). DOI: 10.1016/j.cma.2023.115981
HAL preprint hal-03930849, arXiv preprint 2301.03272 [math.NA]

4) D. A. Di Pietro and J. Droniou
An arbitrary-order discrete de Rham complex on polyhedral meshes: Exactness, Poincaré inequalities, and consistency
Found. Comput. Math., 2023, 23:85–164. DOI: 10.1007/s10208-021-09542-8
arXiv preprint 2101.04940 [math.NA]

5) D. Castañón Quiroz and D. A. Di Pietro
A pressure-robust HHO method for the solution of the incompressible Navier–Stokes equations on general meshes
IMA J. Numer. Anal., 2023. Published online. DOI: 10.1093/imanum/drad007
HAL preprint hal-03608248, arXiv preprint 2203.07180 [math.NA]

6) D. A. Di Pietro and J. Droniou
Homological- and analytical-preserving serendipity framework for polytopal complexes, with application to the DDR method
ESAIM: Math. Model Numer. Anal., 2023, 57(1):191–225. DOI: 10.1051/m2an/2022067
HAL preprint hal-03598859, arXiv preprint 2203.02939 [math.NA]

7) D. A. Di Pietro, P. Matalon, P. Mycek, and U. Rüde
High-order multigrid strategies for HHO discretizations of elliptic equations
Numer. Linear Algebra with Appl., 2023, 30(e2456). DOI: 10.1002/nla.2456
HAL preprint hal-03531293

8) M. Botti, D. A. Di Pietro, and M. Salah
A serendipity fully discrete div-div complex on polygonal meshes
Comptes Rendus Mécanique, 2023, 351(S1). DOI: 10.5802/crmeca.150
HAL preprint hal-03723495, arXiv preprint 2207.07194 [math.NA]

9) D. A. Di Pietro and J. Droniou
A fully discrete plates complex on polygonal meshes with application to the Kirchhoff–Love problem
Math. Comp., 2023, 92(339):51–77. DOI: 10.1090/mcom/3765
HAL preprint hal-03504496, arXiv preprint 2112.14497 [math.NA]

10) D. A. Di Pietro, F. Hülsemann, P. Matalon, P. Mycek, U. Rüde, and D. Ruiz
Algebraic multigrid preconditioner for statically condensed systems arising from lowest-order hybrid discretizations
SIAM J. Sci. Comput., 2022. Published online. DOI: 10.1137/21M1429849. URL: https://hal.archives-ouvertes.fr/hal-03272468
HAL preprint hal-03272468

11) D. A. Di Pietro and J. Droniou
A discrete de Rham method for the Reissner–Mindlin plate bending problem on polygonal meshes
Comput. Math. Appl., 2022, 125:136–149. DOI: 10.1016/j.camwa.2022.08.041
HAL preprint hal-03234088, arXiv preprint 2105.11773 [math.NA]

12) L. Beirão da Veiga, F. Dassi, D. A. Di Pietro, and J. Droniou
Arbitrary-order pressure-robust DDR and VEM methods for the Stokes problem on polyhedral meshes
Comput. Meth. Appl. Mech. Engrg., 2022, 397(115061). DOI: 10.1016/j.cma.2022.115061. URL: https://authors.elsevier.com/a/1fChmAQEIzVqH
HAL preprint hal-03491878, arXiv preprint 2112.0970

13) D. A. Di Pietro, I. Fontana, and K. Kazymyrenko
A posteriori error estimates via equilibrated stress reconstructions for contact problems approximated by Nitsche's method
Comput. Math. Appl., 2022, 111:61–80. DOI: 10.1016/j.camwa.2022.02.008. URL: https://authors.elsevier.com/c/1egEh3CDPQ2-a5
HAL preprint hal-03354078, arXiv preprint 2109.11944 [math.NA]

14) F. Chave, D. A. Di Pietro, and S. Lemaire
A discrete Weber inequality on three-dimensional hybrid spaces with application to the HHO approximation of magnetostatics
Math. Models Methods Appl. Sci., 2022, 32(1):175–207. DOI: 10.1142/S0218202522500051
HAL preprint hal-02892526, arXiv preprint 2007.03485 [math.NA]

15) L. Botti and D. A. Di Pietro
$p$-Multilevel preconditioners for HHO discretizations of the Stokes equations with static condensation
Commun. Appl. Math. Comput., 2022, 4(3):783–822. DOI: 10.1007/s42967-021-00142-5
HAL preprint hal-02951823, arXiv preprint 2009.13840

16) L. Botti, M. Botti, and D. A. Di Pietro
An abstract analysis framework for monolithic discretisations of poroelasticity with application to Hybrid High-Order methods
Comput. Math. Appl., 2021, 91(1):150–175. DOI: 10.1016/j.camwa.2020.06.004
HAL preprint hal-02398946, arXiv preprint 1912.03665 [math.NA]

17) M. Botti, D. Castañón Quiroz, D. A. Di Pietro, and A. Harnist
A Hybrid High-Order method for creeping flows of non-Newtonian fluids
ESAIM: Math. Model Numer. Anal., 2021, 55(5):2045–2073. DOI: 10.1051/m2an/2021051
HAL preprint hal-02519233, arXiv preprint 2003.13467 [math.NA]

18) D. Castañón Quiroz, D. A. Di Pietro, and A. Harnist
A Hybrid High-Order method for incompressible flows of non-Newtonian fluids with power-like convective behaviour
IMA J. Numer. Anal., 2021. Published online. DOI: 10.1093/imanum/drab087
HAL preprint hal-03273118, arXiv preprint 2106.14950 [math.NA]

19) D. A. Di Pietro, J. Droniou, and A. Harnist
Improved error estimates for Hybrid High-Order discretizations of Leray–Lions problems
Calcolo, 2021, 58(19). DOI: 10.1007/s10092-021-00410-z
HAL preprint hal-03049154, arXiv preprint 2012.05122 [math.NA]

20) D. A. Di Pietro and J. Droniou
An arbitrary-order method for magnetostatics on polyhedral meshes based on a discrete de Rham sequence
J. Comput. Phys., 2021, 429(109991). DOI: 10.1016/j.jcp.2020.109991
HAL preprint hal-02573274, arXiv preprint 2005.06890 [math.NA]

21) D. A. Di Pietro, F. Hülsemann, P. Matalon, P. Mycek, U. Rüde, and D. Ruiz
Towards robust, fast solutions of elliptic equations on complex domains through HHO discretizations and non-nested multigrid methods
Internat. J. Numer. Methods Engrg., 2021, 122(22):6576–6595. DOI: 10.1002/nme.6803
HAL preprint hal-03163476

22) D. A. Di Pietro, F. Hülsemann, P. Matalon, P. Mycek, U. Rüde, and D. Ruiz
An $h$-multigrid method for Hybrid High-Order discretizations
SIAM J. Sci. Comput., 2021, 43(5):S839–S861. DOI: 10.1137/20M1342471
HAL preprint hal-02434411

23) M. Botti, D. A. Di Pietro, O. Le Maître, and P. Sochala
Numerical approximation of poroelasticity with random coefficients using Polynomial Chaos and Hybrid High-Order methods
Comput. Meth. Appl. Mech. Engrg., 2020, 361(112736). DOI: 10.1016/j.cma.2019.112736
HAL preprint hal-02081647, arXiv preprint 1903.11885 [math.NA]

24) M. Botti, D. A. Di Pietro, and P. Sochala
A Hybrid High-Order discretisation method for nonlinear poroelasticity
Comput. Meth. Appl. Math., 2020, 20(2):227–249. DOI: 10.1515/cmam-2018-0142
HAL preprint hal-01785810, arXiv preprint 1906.00757 [math.NA]

25) D. Castañón Quiroz and D. A. Di Pietro
A Hybrid High-Order method for the incompressible Navier–Stokes problem robust for large irrotational body forces
Comput. Math. Appl., 2020, 79(8):2655–2677. DOI: 10.1016/j.camwa.2019.12.005
HAL preprint hal-02151236

26) D. A. Di Pietro, J. Droniou, and F. Rapetti
Fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra
Math. Models Methods Appl. Sci., 2020, 30(9):1809-1855. DOI: 10.1142/S0218202520500372
HAL preprint hal-02356810, arXiv preprint 1911.03616 [math.NA]

27) M. Botti, D. A. Di Pietro, and A. Guglielmana
A low-order nonconforming method for linear elasticity on general meshes
Comput. Meth. Appl. Mech. Engrg., 2019, 354:96–118. DOI: 10.1016/j.cma.2019.05.031
HAL preprint hal-02009407, arXiv preprint 1902.02316 [math.NA]

28) L. Botti, D. A. Di Pietro, and J. Droniou
A Hybrid High-Order method for the incompressible Navier–Stokes equations based on Temam's device
J. Comput. Phys., 2019, 376:786–816. DOI: 10.1016/j.jcp.2018.10.014
HAL preprint hal-01867134, arXiv preprint 1807.07345 [math.NA]

29) F. Chave, D. A. Di Pietro, and L. Formaggia
A Hybrid High-Order method for passive transport in fractured porous media
Int. J. Geomath., 2019, 10(12). DOI: 10.1007/s13137-019-0114-x. URL: https://rdcu.be/bjHYw
HAL preprint hal-01784181

30) T. Lelièvre, S. Perotto, G. Rozza, D. A. Di Pietro, A. Ern, and L. Formaggia
Preface: Special Issue on Model Reduction
J. Sci. Comput., 2019, 81:1–2. [Editorial]. DOI: 10.1007/s10915-019-01037-7

31) J. Aghili and D. A. Di Pietro
An advection-robust Hybrid High-Order method for the Oseen problem
J. Sci. Comput., 2018, 77(3):1310–1338. DOI: 10.1007/s10915-018-0681-2
HAL preprint hal-01658263, arXiv preprint 1712.02625 [math.NA]

32) D. Boffi and D. A. Di Pietro
Unified formulation and analysis of mixed and primal discontinuous skeletal methods on polytopal meshes
ESAIM: Math. Model Numer. Anal., 2018, 52(1):1–28. DOI: 10.1051/m2an/2017036
HAL preprint hal-01365938, arXiv preprint 1609.04601 [math.NA]

33) F. Bonaldi, D. A. Di Pietro, G. Geymonat, and F. Krasucki
A Hybrid High-Order method for Kirchhoff–Love plate bending problems
ESAIM: Math. Model Numer. Anal., 2018, 52(2):393–421. DOI: 10.1051/m2an/2017065
HAL preprint hal-01541389, arXiv preprint 1706.06781 [math.NA]

34) L. Botti, D. A. Di Pietro, and J. Droniou
A Hybrid High-Order discretisation of the Brinkman problem robust in the Darcy and Stokes limits
Comput. Meth. Appl. Mech. Engrg., 2018, 341:278–310. DOI: 10.1016/j.cma.2018.07.004
HAL preprint hal-01746367, arXiv preprint 1803.10964 [math.NA]

35) L. Botti and D. A. Di Pietro
Assessment of Hybrid High-Order methods on curved meshes and comparison with discontinuous Galerkin methods
J. Comput. Phys., 2018, 370:58–84. DOI: 10.1016/j.jcp.2018.05.017
HAL preprint hal-01581883

36) F. Chave, D. A. Di Pietro, and L. Formaggia
A Hybrid High-Order method for Darcy flows in fractured porous media
SIAM J. Sci. Comput., 2018, 40(2):A1063–A1094. DOI: 10.1137/17M1119500
HAL preprint hal-01482925

37) M. Cicuttin, D. A. Di Pietro, and A. Ern
Implementation of Discontinuous Skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming
J. Comput. Appl. Math., 2018, 344:852–874. DOI: 10.1016/j.cam.2017.09.017
HAL preprint hal-01429292

38) D. A. Di Pietro, J. Droniou, and G. Manzini
Discontinuous Skeletal Gradient Discretisation methods on polytopal meshes
J. Comput. Phys., 2018, 355:397–425. DOI: 10.1016/j.jcp.2017.11.018
HAL preprint hal-01564598, arXiv preprint 1706.09683 [math.NA]

39) D. A. Di Pietro and J. Droniou
A third Strang lemma and an Aubin–Nitsche trick for schemes in fully discrete formulation
Calcolo, 2018, 55(40). DOI: 10.1007/s10092-018-0282-3. URL: https://rdcu.be/5L8F
HAL preprint hal-01778044, arXiv preprint 1804.09484 [math.NA]

40) D. A. Di Pietro and S. Krell
A Hybrid High-Order method for the steady incompressible Navier–Stokes problem
J. Sci. Comput., 2018, 74(3):1677–1705. DOI: 10.1007/s10915-017-0512-x
HAL preprint hal-01349519, arXiv preprint 1607.08159 [math.NA]

41) D. A. Di Pietro and F. Marche
Weighted Interior Penalty discretization of fully nonlinear and weakly dispersive free surface shallow water flows
J. Comput. Phys., 2018, 355:285–309. DOI: 10.1016/j.jcp.2017.11.009
HAL preprint hal-01566446

42) J. Aghili, D. A. Di Pietro, and B. Ruffini
An $hp$-Hybrid High-Order method for variable diffusion on general meshes
Comput. Meth. Appl. Math., 2017, 17(3):359–376. DOI: 10.1515/cmam-2017-0009
HAL preprint hal-01290251

43) M. Botti, D. A. Di Pietro, and P. Sochala
A Hybrid High-Order method for nonlinear elasticity
SIAM J. Numer. Anal., 2017, 55(6):2687–2717. DOI: 10.1137/16M1105943
HAL preprint hal-01539510, arXiv preprint 1707.02154 [math.NA]

44) D. A. Di Pietro and J. Droniou
$W^{s,p}$-approximation properties of elliptic projectors on polynomial spaces, with application to the error analysis of a Hybrid High-Order discretisation of Leray–Lions problems
Math. Models Methods Appl. Sci., 2017, 27(5):879–908. DOI: 10.1142/S0218202517500191
HAL preprint hal-01326818, arXiv preprint 1606.02832 [math.NA]

45) D. A. Di Pietro and J. Droniou
A Hybrid High-Order method for Leray–Lions elliptic equations on general meshes
Math. Comp., 2017, 86(307):2159–2191. DOI: 10.1090/mcom/3180
HAL preprint hal-01183484, arXiv preprint 1508.01918 [math.NA]

46) D. A. Di Pietro and A. Ern
Arbitrary-order mixed methods for heterogeneous anisotropic diffusion on general meshes
IMA J. Numer. Anal., 2017, 37(1):40–63. DOI: 10.1093/imanum/drw003
HAL preprint hal-00918482

47) D. A. Di Pietro, B. Kapidani, R. Specogna, and F. Trevisan
An arbitrary-order discontinuous skeletal method for solving electrostatics on general polyhedral meshes
IEEE Transactions on Magnetics, 2017, 53(6):1–4. DOI: 10.1109/TMAG.2017.2666546
HAL preprint hal-01399505

48) R. Riedlbeck, D. A. Di Pietro, A. Ern, S. Granet, and K. Kazymyrenko
Stress and flux reconstruction in Biot's poro-elasticity problem with application to a posteriori error analysis
Comput. Math. Appl., 2017, 73(7):1593–1610. DOI: 10.1016/j.camwa.2017.02.005
HAL preprint hal-01366646

49) D. Boffi, M. Botti, and D. A. Di Pietro
A nonconforming high-order method for the Biot problem on general meshes
SIAM J. Sci. Comput., 2016, 38(3):A1508–A1537. DOI: 10.1137/15M1025505
HAL preprint hal-01162976, arXiv preprint 1506.03722 [math.NA]

50) F. Chave, D. A. Di Pietro, F. Marche, and F. Pigeonneau
A Hybrid High-Order method for the Cahn–Hilliard problem in mixed form
SIAM J. Numer. Anal., 2016, 54(3):1873–1898. DOI: 10.1137/15M1041055
HAL preprint hal-01203733, arXiv preprint 1509.07384 [math.NA]

51) B. Cockburn, D. A. Di Pietro, and A. Ern
Bridging the Hybrid High-Order and Hybridizable Discontinuous Galerkin methods
ESAIM: Math. Model Numer. Anal., 2016, 50(3):635–650. DOI: 10.1051/m2an/2015051
HAL preprint hal-01115318

52) D. A. Di Pietro, A. Ern, A. Linke, and F. Schieweck
A discontinuous skeletal method for the viscosity-dependent Stokes problem
Comput. Meth. Appl. Mech. Engrg., 2016, 306:175–195. DOI: 10.1016/j.cma.2016.03.033
HAL preprint hal-01244387

53) D. A. Di Pietro and R. Specogna
An a posteriori-driven adaptive Mixed High-Order method with application to electrostatics
J. Comput. Phys., 2016, 326(1):35–55. DOI: 10.1016/j.jcp.2016.08.041
HAL preprint hal-01310313

54) J. Aghili, S. Boyaval, and D. A. Di Pietro
Hybridization of mixed high-order methods on general meshes and application to the Stokes equations
Comput. Meth. Appl. Math., 2015, 15(2):111–134. DOI: 10.1515/cmam-2015-0004
HAL preprint hal-01009723

55) J. Bonelle, D. A. Di Pietro, and A. Ern
Low-order reconstruction operators on polyhedral meshes: Application to Compatible Discrete Operator schemes
Computer Aided Geometric Design, 2015, 35–36:27–41. DOI: 10.1016/j.cagd.2015.03.015
HAL preprint hal-01097311

56) D. A. Di Pietro, J. Droniou, and A. Ern
A discontinuous-skeletal method for advection-diffusion-reaction on general meshes
SIAM J. Numer. Anal., 2015, 53(5):2135–2157. DOI: 10.1137/140993971
HAL preprint hal-01079342, arXiv preprint 1411.0098 [math.NA]

57) D. A. Di Pietro and A. Ern
Equilibrated tractions for the Hybrid High-Order method
C. R. Acad. Sci. Paris, Ser. I, 2015, 353:279–282. DOI: 10.1016/j.crma.2014.12.009
HAL preprint hal-01079026, arXiv preprint 1411.0094 [math.NA]

58) D. A. Di Pietro and A. Ern
Hybrid high-order methods for variable-diffusion problems on general meshes
C. R. Acad. Sci. Paris, Ser. I, 2015, 353:31–34. DOI: 10.1016/j.crma.2014.10.013
HAL preprint hal-01023302

59) D. A. Di Pietro and A. Ern
A hybrid high-order locking-free method for linear elasticity on general meshes
Comput. Meth. Appl. Mech. Engrg., 2015, 283:1–21. DOI: 10.1016/j.cma.2014.09.009
HAL preprint hal-00979435

60) D. A. Di Pietro and S. Lemaire
An extension of the Crouzeix–Raviart space to general meshes with application to quasi-incompressible linear elasticity and Stokes flow
Math. Comp., 2015, 84(291):1–31. DOI: 10.1090/S0025-5718-2014-02861-5
HAL preprint hal-00753660

61) D. A. Di Pietro, M. Vohralík, and S. Yousef
Adaptive regularization, linearization, discretization, and a posteriori error control for the two-phase Stefan problem
Math. Comp., 2015, 84(291):153–186. DOI: 10.1090/S0025-5718-2014-02854-8
HAL preprint hal-00690862

62) D. A. Di Pietro, A. Ern, and S. Lemaire
An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators
Comput. Meth. Appl. Math., 2014, 14(4):461–472. Open access (editor's choice). DOI: 10.1515/cmam-2014-0018
HAL preprint hal-00978198

63) D. A. Di Pietro, E. Flauraud, M. Vohralík, and S. Yousef
A posteriori error estimates, stopping criteria, and adaptivity for multiphase compositional Darcy flows in porous media
J. Comput. Phys., 2014, 274:163–187. DOI: 10.1016/j.jcp.2014.06.061
HAL preprint hal-00839487

64) D. A. Di Pietro, M. Vohralík, and S. Yousef
An a posteriori-based, fully adaptive algorithm for thermal multiphase compositional flows in porous media with adaptive mesh refinement
Comput. Math. Appl., 2014, 68(12):2331–2347. DOI: 10.1016/j.camwa.2014.08.008
HAL preprint hal-00856437

65) D. A. Di Pietro and M. Vohralík
A review of recent advances in discretization methods, a posteriori error analysis, and adaptive algorithms for numerical modeling in geosciences
Oil & Gas Science and Technology, 2014, 69(4):701–730. DOI: 10.2516/ogst/2013158
HAL preprint hal-00783068

66) D. A. Di Pietro, J.-M. Gratien, and C. Prud'homme
A domain-specific embedded language in C++ for lowest-order discretizations of diffusive problems on general meshes
BIT Numerical Mathematics, 2013, 53(1):111–152. DOI: 10.1007/s10543-012-0403-3
HAL preprint hal-00654406

67) D. A. Di Pietro and S. Nicaise
A locking-free discontinuous Galerkin method for linear elasticity in locally nearly incompressible heterogeneous media
App. Num. Math., 2013, 63:105–116. DOI: 10.1016/j.apnum.2012.09.009
HAL preprint hal-00685020

68) D. A. Di Pietro
On the conservativity of cell centered Galerkin methods
C. R. Acad. Sci. Paris, Ser. I, 2013, 351(3–4):155–159. DOI: 10.1016/j.crma.2013.03.001
HAL preprint hal-00781510

69) F. Bassi, L. Botti, A. Colombo, D. A. Di Pietro, and P. Tesini
On the flexibility of agglomeration based physical space discontinuous Galerkin discretizations
J. Comput. Phys., 2012, 231(1):45–65. DOI: 10.1016/j.jcp.2011.08.018
HAL preprint hal-00562219

70) D. A. Di Pietro and A. Ern
Analysis of a discontinuous Galerkin method for heterogeneous diffusion problems with low-regularity solutions
Numer. Meth. for PDEs, 2012, 28(4):1161–1177. DOI: 10.1002/num.20675
HAL preprint hal-00514387

71) D. A. Di Pietro
Cell centered Galerkin methods for diffusive problems
ESAIM: Math. Model Numer. Anal., 2012, 46(1):111–144. DOI: 10.1051/m2an/2011016
HAL preprint hal-00511125

72) L. Botti and D. A. Di Pietro
A pressure-correction scheme for convection-dominated incompressible flows with discontinuous velocity and continuous pressure
J. Comput. Phys., 2011, 230(3):572–585. DOI: 10.1016/j.jcp.2010.10.004
HAL preprint hal-00458293

73) D. A. Di Pietro
A compact cell-centered Galerkin method with subgrid stabilization
C. R. Acad. Sci. Paris, Ser. I, 2011, 349(1–2):93–98. DOI: 10.1016/j.crma.2010.11.017
HAL preprint hal-00476222

74) L. Agélas, D. A. Di Pietro, and J. Droniou
The G method for heterogeneous anisotropic diffusion on general meshes
ESAIM: Math. Model Numer. Anal., 2010, 44(4):597–625. DOI: 10.1051/m2an/2010021
HAL preprint hal-00342739

75) L. Agélas, D. A. Di Pietro, R. Eymard, and R. Masson
An abstract analysis framework for nonconforming approximations of diffusion problems on general meshes
IJFV International Journal on Finite Volumes, 2010, 7(1):1–29
HAL preprint hal-00318390

76) D. A. Di Pietro and A. Ern
Discrete functional analysis tools for discontinuous Galerkin methods with application to the incompressible Navier–Stokes equations
Math. Comp., 2010, 79:1303–1330. DOI: 10.1090/S0025-5718-10-02333-1
HAL preprint hal-00278925

77) D. A. Di Pietro
Cell centered Galerkin methods
C. R. Acad. Sci. Paris, Ser. I, 2010, 348(1–2):31–34. DOI: 10.1016/j.crma.2009.11.012
HAL preprint hal-00398782

78) D. A. Di Pietro and A. Veneziani
Expression template implementation of continuous and discontinuous Galerkin methods
Comp. Vis. in Sci., 2009, 12:421–436. DOI: 10.1007/s00791-008-0117-x
HAL preprint hal-01818198

79) D. A. Di Pietro, A. Ern, and J.-L. Guermond
Discontinuous Galerkin methods for anisotropic semi-definite diffusion with advection
SIAM J. Numer. Anal., 2008, 46(2):805–831. DOI: 10.1137/060676106
HAL preprint hal-01818201

80) F. Bassi, A. Crivellini, D. A. Di Pietro, and S. Rebay
An implicit high-order discontinuous Galerkin method for steady and unsteady incompressible flows
Comp. & Fl., 2007, 36(10):1529–1546. DOI: 10.1016/j.compfluid.2007.03.012
HAL preprint hal-01818204

81) D. A. Di Pietro
Analysis of a discontinuous Galerkin approximation of the Stokes problem based on an artificial compressibility flux
Int. J. Num. Meth. Fluids, 2007, 55(8):793–813. DOI: 10.1002/fld.1495
HAL preprint hal-01818207

82) F. Bassi, A. Crivellini, D. A. Di Pietro, and S. Rebay
An artificial compressibility flux for the discontinuous Galerkin solution of the incompressible Navier-Stokes equations
J. Comput. Phys., 2006, 218(2):794–815. DOI: 10.1016/j.jcp.2006.03.006
HAL preprint hal-01818209

83) D. A. Di Pietro, S. Lo Forte, and N. Parolini
Mass preserving finite element implementations of the level set method
App. Num. Math., 2006, 56:1179–1195. DOI: 10.1016/j.apnum.2006.03.003
HAL preprint hal-01818211

84) G. E. Cossali, D. A. Di Pietro, and M. Marengo
Comparison of four analytical and numerical models for a microchannel heat sink
Int. J. Heat and Tech., 2003, 21(2):31–42
HAL preprint hal-01820286

Book chapters (4)

1) L. Botti, M. Botti, and D. A. Di Pietro
A Hybrid High-Order method for multiple-network poroelasticity
in Polyhedral Methods in Geosciences, D. A. Di Pietro, L. Formaggia, R. Masson eds., Springer, 2021, p. 227–258
DOI: 10.1007/978-3-030-69363-3_6 , ISBN: 978-3-030-69362-6
HAL preprint hal-02461755

2) D. A. Di Pietro, A. Ern, and L. Formaggia
An introduction to recent developments in numerical methods for partial differential equations
in Numerical Methods for PDEs: State of the Art Techniques, D. A. Di Pietro, A. Ern, L. Formaggia eds., Springer, 2018, p. 1–4
DOI: 10.1007/978-3-319-94676-4_1 , ISBN: 978-3-319-94675-7 (Print) 978-3-319-94676-4 (eBook)
HAL preprint hal-01490524, arXiv preprint 1703.05136 [math.NA]

3) D. A. Di Pietro and R. Tittarelli
An introduction to Hybrid High-Order methods
in Numerical Methods for PDEs: State of the Art Techniques, D. A. Di Pietro, A. Ern, L. Formaggia eds., Springer, 2018, p. 75–128
DOI: 10.1007/978-3-319-94676-4_4 , ISBN: 978-3-319-94675-7 (Print) 978-3-319-94676-4 (eBook)
HAL preprint hal-01490524, arXiv preprint 1703.05136 [math.NA]

4) D. A. Di Pietro, A. Ern, and S. Lemaire
A review of Hybrid High-Order methods: formulations, computational aspects, comparison with other methods
in Building bridges: Connections and challenges in modern approaches to numerical partial differential equations, Barrenechea, G. and Brezzi, F. and Cangiani, A. and Georgoulis, M. eds., Springer, 2016, p. 205–236
DOI: 10.1007/978-3-319-41640-3 , ISBN: 978-3-319-41638-0 (Print) 978-3-319-41640-3 (eBook)
HAL preprint hal-01163569

Preprints (3)

1) D. A. Di Pietro and M.-L. Hanot
A discrete three-dimensional divdiv complex on polyhedral meshes with application to a mixed formulation of the biharmonic problem
HAL preprint hal-04093192, arXiv preprint 2305.05729 [math.NA], May 2023

2) F. Bonaldi, D. A. Di Pietro, J. Droniou, and K. Hu
An exterior calculus framework for polytopal methods
HAL preprint hal-04037653, arXiv preprint 2303.11093 [math.NA], March 2023

3) I. Fontana, K. Kazymyrenko, and D. A. Di Pietro
Hyperelastic nature of the Hoek–Brown criterion
HAL preprint hal-03501788, December 2021

Proceedings (19)

1) F. Chave, D. A. Di Pietro, and S. Lemaire
A three-dimensional Hybrid High-Order method for magnetostatics
Finite Volumes for Complex Applications IX – Methods, Theoretical Aspects, Examples, 2020 p. 255–263
DOI: 10.1007/978-3-030-43651-3_22
Preprint hal-02407175

2) M. Botti, D. A. Di Pietro, and P. Sochala
A nonconforming high-order method for nonlinear poroelasticity
Finite Volumes for Complex Applications VIII – Hyperbolic, Elliptic and Parabolic Problems, 2017 p. 537–546
DOI: 10.1007/978-3-319-57397-7
Preprint hal-01439165

3) F. Chave, D. A. Di Pietro, and F. Marche
A Hybrid High-Order method for the convective Cahn–Hilliard problem in mixed form
Finite Volumes for Complex Applications VIII – Hyperbolic, Elliptic and Parabolic Problems, 2017 p. 517–526
DOI: 10.1007/978-3-319-57397-7
Preprint hal-01477247

4) D. A. Di Pietro and S. Krell
Benchmark session: The 2D Hybrid High-Order method
Finite Volumes for Complex Applications VIII – Methods and Theoretical Aspects, 2017 p. 91–106
DOI: 10.1007/978-3-319-57397-7
Preprint hal-01818217

5) R. Riedlbeck, D. A. Di Pietro, and A. Ern
Equilibrated stress reconstruction for linear elasticity problems with application to a posteriori error analysis
Finite Volumes for Complex Applications VIII – Methods and Theoretical Aspects, 2017 p. 293–302
Preprint hal-01433841

6) D. A. Di Pietro, R. Eymard, S. Lemaire, and R. Masson
Hybrid finite volume discretization of linear elasticity models on general meshes
Finite Volumes for Complex Applications VI, 2011 p. 331–339
DOI: 10.1007/978-3-642-20671-9_35
Preprint hal-00795201

7) D. A. Di Pietro and J.-M. Gratien
Lowest order methods for diffusive problems on general meshes: A unified approach to definition and implementation
Finite Volumes for Complex Applications VI, 2011 p. 3–19. Invited paper
DOI: 10.1007/978-3-642-20671-9_84
Preprint hal-00562500

8) D. A. Di Pietro, M. Vohralík, and C. Widmer
An a posteriori error estimator for a finite volume discretization of two-phase flow
Finite Volumes for Complex Applications VI, 2011 p. 341–349
DOI: 10.1007/978-3-642-20671-9_36

9) L. Agélas, D. A. Di Pietro, and I. Kapyrin
A comparison of last generation cell centered finite volume methods on challenging three dimensional problems
Proceedings of the 3rd International Conference on Approximation Methods and numerical Modeling in Environment and Natural Resources, 2009

10) L. Agélas, D. A. Di Pietro, I. Kapyrin, and R. Masson
Generalized L-scheme for the discretization of diffusion fluxes on general meshes
Proceedings of the 11th European Conference on the Mathematics of Oil Recovery, 2008

11) L. Agélas, D. A. Di Pietro, R. Eymard, and R. Masson
A general framework for non-conforming approximations of the single phase Darcy equation
Proceedings of the 11th European Conference on the Mathematics of Oil Recovery, 2008

12) L. Agélas, D. A. Di Pietro, I. Kapyrin, and R. Masson
The MPFA G scheme for heterogeneous anisotropic diffusion problems on general meshes
Proceedings of the 11th European Conference on the Mathematics of Oil Recovery, 2008

13) L. Agélas, D. A. Di Pietro, and R. Masson
A symmetric and coercive finite volume scheme for multiphase porous media flow with applications in the oil industry
Finite Volumes for Complex Applications V, 2008 p. 35–52. Invited paper
Preprint hal-01818220
ISBN: 978-1-84821-035-6

14) L. Agélas and D. A. Di Pietro
A symmetric finite volume scheme for anisotropic heterogeneous second-order elliptic problems
Finite Volumes for Complex Applications V, 2008 p. 705–716
ISBN: 978-1-84821-035-6

15) D. A. Di Pietro and A. Ern
A discontinuous Galerkin flux for anisotropic heterogeneous second-order elliptic problems
Finite Volumes for Complex Applications V, 2008 p. 777–793
Preprint hal-01818221
ISBN: 978-1-84821-035-6

16) S. Mundal, D. A. Di Pietro, and I. Aavatsmark
Compact-stencil MPFA method for heterogeneous highly-anisotropic second order elliptic problems
Finite Volumes for Complex Applications V, 2008 p. 905–918
Preprint hal-01818222
ISBN: 978-1-84821-035-6

17) F. Bassi, A. Crivellini, D. A. Di Pietro, and S. Rebay
A high-order discontinuous Galerkin solver for 3D aerodynamic turbulent flows
ECCOMAS CFD 2006 Proceedings (Egmond an Zee, Netherlands), 2006

18) G. E. Cossali, D. A. Di Pietro, and M. Marengo
Analytical and numerical modeling of microchannel heat sinks
Proceedings of the First International Conference on Microchannels and Minichannels (Rochester, New York), 2003

19) G. E. Cossali, D. A. Di Pietro, and M. Marengo
Design of a microchannel cooling system for BTeV particle detector
Proceedings of the 8th International Workshop on Thermal Investigations of ICs and Systems (Madrid, Spain), 2002

Theses (2)

1) D. A. Di Pietro
Méthodes non conformes pour des équations aux dérivées partielles avec diffusion
HDR thesis, Université de Paris-Est, 6 December 2010
Manuscript tel-00550230

2) D. A. Di Pietro
Discontinuous Galerkin methods for the incompressible Navier–Stokes equations
PhD thesis, Università di Bergamo, 3 March 2006

Analyse Numérique 4 (HAX905X)

1. Annexe A et Chapitre 1 : Cadre général
• Rappels
• Strang 3 : Partie 1 et Partie 2
• Maillage
• Espaces de fonctions
• Outils de base. Avant de regarder la vidéo, lire les Sections 1.2.1 et 1.2.2 du livre
2. Chapitre 2 : HHO pour Poisson
• Construction locale
• Stabilisation HHO
• Problème discret
• Formulation flux
• Analyse d'erreur : Partie 1 et Partie 2
3. Sections 5.1 et 5.4 : Compléments
• MHO - Problème discret Partie 1 et Partie 2
• MHO - Hybridation
• Variations
4. Annexe B : Implémentation
• Implémentation et condensation statique

Algèbre Linéaire Numérique (HAX406X)

1. Introduction
2. Chapitre 1 : Rappels et compléments
• Cours 1 (jusqu'à l'Exercice 1.8)
• Cours 2 (de la Proposition 1.9 jusqu'à la Remarque 1.16
• Cours 3 (de l'Exemple 1.17 jusqu'à l'Exemple 1.25)
• Cours 4 (de la Proposition 1.26 jusqu'à la fin de la Section 1.4.1)
• Cours 5 (de la Section 1.4.2 jusqu'à la fin du Chapitre 1)
• TD 1 (preuve de la Proposition 1.48, regarder à la suite du Cours 5)
• TD 2 (Exercices 1.51, 1.52, 1.53)
• TD 3 (Exercices 1.54, 1.55, 1.64)
3. Chapitre 2 : Méthodes directes
• Cours 6 (Sections 2.1.1 et 2.1.2)
• Cours 7 (Section 2.2)
• TP (conditionnement)
• Cours 8 (Section 2.3.1)
• Cours 9 (Sections 2.3.2–2.3.4)
• Cours 10 (Sections 2.3.4–2.4)
• Cours 11 (Exemple 2.19)
• TD 4 (Exercices 2.20 et 2.21, regarder à la suite du Cours 11)
• TD 5 (Exercices 2.22 et 2.23)
4. Chapitre 3 : Méthodes itératives
• Cours 12 (jusqu'à la preuve du Lemme 3.2)
• Cours 13 (fin de la Section 3.1.1 et Section 3.1.2)
• TD 6 (Exercice 3.15)
• TD 7 (Exercice 3.16)
• TD 8 (Exercice 3.17)
5. Compléments
• TP (méthode de la puissance)