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 (68)

1) D. A. Di Pietro, F. Hülsemann, P. Matalon, P. Mycek, U. Rüde, and D. Ruiz
Toward robust, fast solutions of elliptic equations on complex domains through HHO discretizations and non-nested multigrid methods
Internat. J. Numer. Methods Engrg., 2021. Accepted for publication. URL: https://hal.archives-ouvertes.fr/hal-03163476
HAL preprint hal-03163476

2) 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. Accepted for publication. URL: https://hal.archives-ouvertes.fr/hal-02434411
HAL preprint hal-02434411

3) L. Botti and D. A. Di Pietro
$p$-Multilevel preconditioners for HHO discretizations of the Stokes equations with static condensation
Commun. Appl. Math. Comput., 2021. To appear. DOI: 10.1007/s42967-021-00142-5
HAL preprint hal-02951823, arXiv preprint arXiv:2009.13840

4) 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 arXiv:1912.03665

5) 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 arXiv:2012.05122

6) 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 arXiv:2005.06890

7) 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 arXiv:1911.03616

8) D. Castanon 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

9) 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 arXiv:1903.11885

10) 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 arXiv:1906.00757

11) 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

12) 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 arXiv:1902.02316

13) 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 arXiv:1807.07345

14) 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

15) 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 arXiv:1804.09484

16) 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

17) 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 arXiv:1803.10964

18) 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 arXiv:1712.02625

19) 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 arXiv:1609.04601

20) 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 arXiv:1706.06781

21) 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

22) 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 arXiv:1706.09683

23) 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

24) 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 arXiv:1607.08159

25) 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

26) 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

27) 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 arXiv:1707.02154

28) 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 arXiv:1606.02832

29) 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 arXiv:1508.01918

30) 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

31) 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

32) 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

33) 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 arXiv:1506.03722

34) 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 arXiv:1509.07384

35) 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

36) 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

37) 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

38) 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

39) 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

40) 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 arXiv:1411.0098

41) 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 arXiv:1411.0094

42) 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

43) 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

44) 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

45) 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

46) 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

47) 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

48) 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

49) 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

50) 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

51) 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

52) 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

53) 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

54) 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

55) 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

56) 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

57) 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

58) 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

59) 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

60) 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

61) 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

62) 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

63) 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

64) 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

65) 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

66) 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

67) 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

68) 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 arXiv:1703.05136

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 arXiv:1703.05136

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 (6)

1) D. Castanon 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
HAL preprint hal-03273118, arXiv preprint arXiv:2106.14950, June 2021

2) 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
HAL preprint hal-03272468, June 2021

3) D. A. Di Pietro and J. Droniou
A DDR method for the Reissner–Mindlin plate bending problem on polygonal meshes
HAL preprint hal-03234088, arXiv preprint arXiv:2105.11773, May 2021

4) D. A. Di Pietro and J. Droniou
An arbitrary-order discrete de Rham complex on polyhedral meshes: Exactness, Poincaré inequalities, and consistency
arXiv preprint arXiv:2101.04940, January 2021

5) 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
HAL preprint hal-02892526, arXiv preprint arXiv:2007.03485, July 2020

6) M. Botti, D. Castanon Quiroz, D. A. Di Pietro, and A. Harnist
A Hybrid High-Order method for creeping flows of non-Newtonian fluids
HAL preprint hal-02519233, arXiv preprint arXiv:2003.13467, March 2020

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 3 (HMMA358)

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

Modélisation Numérique (HMMA436)

• Notions de base Partie 1 et Partie 2
• La suite de de Rham $L^2$
• Approximations éléments finis

Analyse Numérique Matricielle (HLMA405)

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)