Daniele A. Di Pietro

Last updated: 6/7/2024

About me

Full professor of Numerical Analysis

Corresponding PI of the ERC Synergy NEMESIS ERC logo

Director of Institut Montpelliérain Alexander Grothendieck

Research

Advanced numerical methods for PDEs

A priori and a posteriori error analysis

Fluid and solid mechanics

Modern implementation techniques

Teaching

Analyse Numérique 4

Optimisation

Algèbre Linéaire Numérique


About me

Full name Daniele Antonio Di Pietro
Affiliation Université de Montpellier
Curriculum vitæ CV (PDF format)
Postal address Université de Montpellier
Institut Montpelliérain Alexander Grothendieck
Case courrier 051
place Eugène Bataillon
34090 Montpellier, France
E-mail daniele.di-pietro AT umontpellier.fr

Research

Research unit Institut Montpelliérain Alexander Grothendieck (UMR 5149)
Editorial activity Associate Editor of Numerical Algorithms (Springer), Boletín de la Sociedad Matemática Mexicana (Springer), Electronic Research Archive (AIMSPress)

Editor of two monographs in the Springer SEMA-SIMAI series

Research databases MathSciNet (790640) (requires subscription), Scopus (6603444428), Google Scholar, ORCID (0000-0003-0959-8830)
Highlights MSCA EffECT funded in the 2024 call

The ERC NEMESIS kick-off workshop will take place in Montpellier, 19-21 June 2024

ERC SyG NEMESIS funded in the 2023 call

POEMS 2024 at Inria Paris

ANR HIPOTHEC (PRCE) and MSM$\Phi$ (PRME) funded in the 2023 call

HArDCore, an HHO-oriented C++ library

See also: NAGANA workgroup, POEMS 2022 at Politecnico di Milano, ANR NEMESIS workshop, POEMS 2019 at CIRM, ANR fast4hho, ANR HHOMM, IHP Thematic Quarter Numerical Methods for PDEs

Publications

All in one BibTeX file

book
1) D. A. Di Pietro and J. Droniou
The Hybrid High-Order method for polytopal meshes
Number 19 in Modeling, Simulation and Application
Springer International Publishing, 2020
ISBN: 978-3-030-37202-6
DOI: 10.1007/978-3-030-37203-3
HAL preprint hal-02151813

book
2) D. A. Di Pietro and A. Ern
Mathematical aspects of discontinuous Galerkin methods
Number 69 in Mathématiques \& Applications (Berlin) [Mathematics \& Applications]
Springer, Heidelberg, 2012
ISBN: 978-3-642-22979-4
DOI: 10.1007/978-3-642-22980-0
HAL preprint hal-01820185

book
1) Di Pietro, D. A. and Formaggia, L. and Masson, R.
Polyhedral Methods in Geosciences
Number 27 in SEMA-SIMAI
Springer International Publishing, 2021
ISBN: 978-3-030-69362-6
DOI: 10.1007/978-3-030-69363-3

book
2) Di Pietro, D. A. and Ern, A. and Formaggia, L.
Numerical Methods for PDEs
Number 15 in SEMA-SIMAI
Springer International Publishing, 2018
ISBN: 978-3-319-94675-7
DOI: 10.1007/978-3-319-94676-4
HAL preprint hal-01818426

1) L. Beirão da Veiga, D. A. Di Pietro, and K. B. Haile
A Péclet-robust discontinuous Galerkin method for nonlinear diffusion with advection N
Math. Models Methods Appl. Sci., 2024. Published online. DOI: 10.1142/S0218202524500350
HAL preprint hal-04458310, arXiv preprint 2402.09814 [math.NA]

2) 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
Math. Models Methods Appl. Sci., 2024. Published online. DOI: 10.1142/S0218202524500313
HAL preprint hal-04093192, arXiv preprint 2305.05729 [math.NA]

3) 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., 2024, 44(1):397–434. DOI: 10.1093/imanum/drad007
HAL preprint hal-03608248, arXiv preprint 2203.07180 [math.NA]

4) I. Fontana and D. A. Di Pietro
An a posteriori error analysis based on equilibrated stresses for finite element approximations of frictional contact N
Comput. Meth. Appl. Mech. Engrg., 2024, 425(116950). DOI: 10.1016/j.cma.2024.116950
HAL preprint hal-04375623, arXiv preprint 2401.02944 [math.NA]

5) D. A. Di Pietro, J. Droniou, and J. J. Qian
A pressure-robust Discrete de Rham scheme for the Navier–Stokes equations N
Comput. Meth. Appl. Mech. Engrg., 2024, 421(116765). DOI: 10.1016/j.cma.2024.116765
HAL preprint hal-04375767, arXiv preprint 2401.04456 [math.NA]

6) 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. Published online. DOI: 10.1093/imanum/drad045
HAL preprint hal-03830503, arXiv preprint 2210.15581 [math.NA]

7) 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]

8) 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]

9) 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
HAL preprint hal-04536890, arXiv preprint 2101.04940 [math.NA]

10) 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]

11) 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

12) 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]

13) 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]

14) 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., 2023, 43(1):144–186. DOI: 10.1093/imanum/drab087
HAL preprint hal-03273118

15) 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
HAL preprint hal-03272468

16) 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]

17) 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

18) 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

19) 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

20) 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

21) 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

22) 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

23) 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

24) 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

25) 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

26) 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

27) 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

28) 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

29) 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

30) 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

31) 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

32) 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

33) 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

34) 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

35) 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

36) 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

37) 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

38) 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

39) 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

40) 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

41) 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

42) 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

43) 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

44) 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

45) 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

46) 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

47) 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

48) 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

49) 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

50) 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

51) 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

52) 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

53) 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

54) 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

55) 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

56) 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

57) 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

58) 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

59) 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

60) 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

61) 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

62) 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

63) 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

64) 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

65) 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

66) 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

67) 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

68) 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

69) 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

70) 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

71) 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

72) 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

73) 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

74) 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

75) 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

76) 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

77) 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

78) 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

79) 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

80) 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

81) 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

82) 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

83) 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

84) 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

85) 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

86) 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

87) 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

88) 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

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
HAL preprint hal-01490524

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
HAL preprint hal-01490524

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
HAL preprint hal-01163569

1) L. Botti, M. Botti, D. A. Di Pietro, and F. C. Massa
Stability, convergence, and pressure-robustness of numerical schemes for incompressible flows with hybrid velocity and pressure N
HAL preprint hal-04552438, arXiv preprint 2404.12732, April 2024

2) D. A. Di Pietro, Z. Dong, G. Kanschat, P. Matalon, and A. Rupp
Homogeneous multigrid for hybrid discretizations: application to HHO methods N
HAL preprint hal-04518103, arXiv preprint 2403.15858 [math.NA], March 2024

3) D. A. Di Pietro and M.-L. Hanot
Uniform Poincaré inequalities for the Discrete de Rham complex on general domains N
HAL preprint hal-04220112, arXiv preprint 2309.15667 [math.NA], September 2023

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

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

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

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

Selected recent presentations

1) A new generation of numerical methods for partial differential equations: The NEMESIS project N [slides]
MIPS Colloquia, Montpellier, 19 June 2024

2) Polytopal approximations of Hilbert complexes N [slides]
NEMESIS kick-off workshop, 19 June 2024

3) Hybrid High-Order methods: Convergence analysis and flux formulation N [slides]
IIT Bombay, 13 May 2024. 2h remote PhD course

4) Basic principles of polytopal approximations of partial differential equations N [slides]
Scuola Superiore Meridionale, Napoli, 2 May 2024

5) Hybrid High-Order methods: Introduction and fully discrete analysis framework N [slides]
IIT Bombay, 22 April 2024. 2h remote PhD course

6) An introduction to Discrete de Rham (DDR) methods N [slides]
HIPOTHEC kick-off workshop, 7 March 2024

7) Approssimazione numerica di sistemi fisici N [slides]
Collegio Ghislieri, Pavia, 22 February 2024

8) An introduction to Discrete de Rham (DDR) methods N [slides]
Università di Bergamo, 14 February 2024

9) An introduction to Discrete de Rham (DDR) methods [slides]
LJLL, Université Pierre et Marie Curie, 6 October 2023. 1h seminar

10) An introduction to Discrete de Rham (DDR) methods [slides]
École d'été CEA-EDF-Inria, 29 June 2023. 4h course

11) Discrete de Rham (DDR) methods for continuum mechanics [slides]
Journées d'Occitanie en Mathématiques Appliquées, 8 June 2023

12) Discrete de Rham methods for mixed formulations [slides]
M2P, 30 May 2023

13) Discrete de Rham (DDR) complexes for compatible approximations of physical problems on general meshes [slides]
MOX, Politecnico di Milano, 26 May 2023

14) An introduction to discrete de Rham methods. A polytopal exterior calculus framework [slides]
Journées Ondes du Sud-Ouest, 15 March 2023

15) Hybrid High-Order methods for the incompressible Navier–Stokes equations [slides]
Onera, 9 December 2022

16) A Hybrid High-Order method for the incompressible Navier–Stokes problem robust for large irrotational body forces [slides]
SIAM AN22, 14 July 2022

17) From physical models to advanced numerical methods through de Rham cohomology [slides]
100 years Unione Matematica Italiana / 800 years Università di Padova, 27 May 2022

18) From physical models to advanced numerical methods through de Rham cohomology [slides]
EPFL, 19 January 2022

19) Hybrid High-Order methods for Darcean flows in complex porous media [slides]
SimRace 2021, 2 December 2021. [impermeable fractures], [permeable fractures], [a peculiar fracture pattern]

20) Arbitrary-order fully discrete complexes on polyhedral meshes [slides] [video]
ICOSAHOM 2020 2021, 14 July 2021

21) A discrete exact grad-curl-div complex on generic polyhedral meshes. Part I: Algebraic properties [slides] [video]
USNCCM16 16th U.S. National Congress on Computational Mechanics, 25 July 2021

22) Fully discrete polynomial de Rham complexes on polyhedral meshes with application to magnetostatics [slides]
INdAM workshop Polygonal methods for PDEs: theory and applications, Rome (virtual), 17 May 2021

23) Hybrid High-Order methods for nonlinear problems [slides]
Seminario del Dipartimento di Matematica “Tullio Levi-Civita”, Università di Padova, 13 May 2021. Leray–Lions and nonlinear Stokes problems

24) Hybrid High-Order methods for nonlinear problems [slides]
Bi.discrete seminar, Universität Bielefeld, 6 April 2021. Leray–Lions and nonlinear elasticity problems

25) Fully discrete polynomial de Rham complexes on polyhedral meshes with application to magnetostatics [slides]
SIAM CSE21, 1 March 2021

26) Recent advances on fully discrete methods for polyhedral meshes [video]
WCCM-ECCOMAS 2020, 14 January 2021

27) An arbitrary-order discrete de Rham complex on polyhedral meshes [slides]
Mathematisches Forschungsinstitut Oberwolfach, Nonstandard Finite Element Methods workshop, 12 January 2021

28) Fully discrete polynomial de Rham sequences of arbitrary degree on polyhedral meshes [slides]
Université de Montpellier, 12 December 2020

29) Fully discrete polynomial de Rham sequences of arbitrary degree on polyhedral meshes [slides]
Università di Padova, 6 November 2020

30) Hybrid High-Order methods for poroelasticity [slides]
IFP Energies Nouvelles, 4 December 2019

31) Hybrid High-Order methods for poroelasticity [slides]
Université de Franche-Comté, 2 October 2019

32) Recent advances on Hybrid High-Order methods for problems in incompressible fluid mechanics [slides]
ICIAM 2019, 16 July 2019

33) Hybrid High-Order methods for diffusion problems on polytopes and curved elements [slides]
MAFELAP 2019, 19 June 2019

34) An introduction to Hybrid High-Order methods with applications to incompressible fluid mechanics [slides]
Université de Nice Sophia Antipolis, 16 May 2019

35) Hybrid High-Order methods for elasticity [slides]
POEMS 2019, 3 May 2019

36) An introduction to Hybrid High-Order methods with applications to incompressible fluid mechanics [slides]
SISSA, 7 March 2019

37) A Hybrid High-Order method for incompressible Navier–Stokes equations based on Temam's device [slides]
Università di Udine, 30 October 2018

38) A Hybrid High-Order method for incompressible Navier–Stokes equations based on Temam's device [slides]
EDF, 28 June 2018

39) An introduction to Hybrid High-Order methods with application to the incompressible Navier–Stokes equations [slides]
Montpellier, 19 June 2018

40) A non-standard application of the Raviart–Thomas–Nédélec element: A HHO method for the Brinkman problem robust in the Darcy and Stokes limits [slides]
CANUM 2018, 29 May 2018. See also here for a stable high-order gradient reconstruction on general meshes based on the Raviart–Thomas–Nédélec element

41) An introduction to the convergence analysis of discretisation methods for PDEs with application to Hybrid High-Order methods [slides]
Università di Bergamo, 10-11 May 2018. See also here for the discrete analysis framework and here for an introduction to HHO methods

42) An introduction to Hybrid High-Order methods [slides]
CERFACS, 9 February 2018

43) An introduction to Hybrid High-Order methods - Nonlinear elasticity and poroelasticity [slides]
Università di Bergamo, 19 December 2017

44) An introduction to Hybrid High-Order methods - Nonlinear elasticity and poroelasticity [slides]
Journées Multiphasiques et Incertitudes, Nantes, 14 November 2017

45) Recent advances on Hybrid High-Order methods for linear and nonlinear problems [slides]
POEMS 2017, Milan, 5 July 2017

46) Recent advances on Hybrid High-Order methods for nonlinear problems [slides]
MOX, Politecnico di Milano, 20 December 2016

47) Hybrid High-Order methods [slides]
Institut Henri Poincaré thematic quarter Numerical Methods for PDEs, 13-14 September 2016

48) A Hybrid High-Order method for Leray–Lions equations [slides]
MAFELAP 2016, 16 June 2016

49) Bridging the Hybrid High-Order and Hybridizable Discontinuous Galerkin Methods [slides]
MAFELAP 2016, 15 June 2016

50) Hybrid High-Order methods on general meshes [slides]
Universität Zürich, 20 April 2016

51) An a posteriori-based fully adaptive algorithm for the two-phase Stefan problem [slides]
Università di Pavia, 23 February 2016

52) A Hybrid High-Order method for locally degenerate advection-diffusion-reaction [slides]
X-DMS 2015, Ferrara, 10 September 2015

53) An introduction to Hybrid High-Order methods [slides]
CEA-EDF-INRIA School New trends in Compatible Discretizations, INRIA Roquencourt, 29 June 2015

54) Hybrid High-Order (HHO) methods on general meshes [slides]
Journée Méthode de Galerkine discontinue et ses applications, CNAM, Paris, 19 June 2015

55) Hybrid and mixed high-order methods [slides]
Università Milano Bicocca, 12 February 2015

56) Hybrid High-Order methods for degenerate advection-diffusion-reaction [slides]
Séminaire Modélisation mathématique et calcul scientifique ICJ, Lyon, 20 January 2015

57) Hybrid high-order methods for quasi-incompressible linear elasticity on general meshes [slides]
WCCM XI, Barcelona, 24 July 2014

58) A family of arbitrary-order mixed methods for anisotropic heterogeneous diffusion [slides]
GT Calcul Scientifique, UM2, 14 February 2014

59) A posteriori error estimates, stopping criteria, and adaptivity for multiphase compositional Darcy flows in porous media [slides]
LATP, Université Aix Marseille, 1 October 2013

60) Discontinuous Galerkin methods and applications [slides]
École de Mécanique des Fluides Numériques, Porquerolles, 2–8 June 2013

61) An extension of the Crouzeix–Raviart and Raviart–Thomas spaces to general meshes [slides]
MOX, Politecnico di Milano, 26 February 2013

62) A hybrid finite volume generalization of the Crouzeix-Raviart element [slides]
GDR MoMaS workshop, Marseille, 15 October 2012

63) Locking-free numerical approximations of the elasticity operator [slides]
Workshop on complex grids and fluid flows, 2 April 2012

64) Cell centered Galerkin methods for diffusive problems on general meshes [slides]
Università di Bergamo, 21 December 2011

65) Recent advances on nonconforming methods for diffusive problems on general meshes [slides]
University of Montpellier 2, 8 November 2011

66) Lowest order methods for diffusive problems on general meshes [slides]
Finite Volumes for Complex Applications VI, Prague, 8 June 2011

67) Nonconforming methods for PDEs with diffusion [slides]
University of Sussex, Brighton, 6 May 2011

Press

Portrait de l'UM (in French)

Portrait “Talents CNRS” (in French)

MaddMaths interview (in Italian)


Teaching

Teaching component Faculté des Sciences
Teaching department Département de Mathématiques
Highlights Master Modélisation et Analyse Numérique

Handouts

Aller à la playlist du cours.

  1. Annexe A et Chapitre 1 : Cadre général
  2. Chapitre 2 : HHO pour Poisson
  3. Sections 5.1 et 5.4 : Compléments
  4. Annexe B : Implémentation

Télécharger tous les documents de cours.

Télécharger les notes du cours (version provisoire permanente). Aller à la playlist du cours.

  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
  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