Books (1)

1) 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

Articles (28)

1) D. Anderson and J. Droniou
An arbitrary order scheme on generic meshes for miscible displacements in porous media
J. Sci. Comput., 2018. To appear

2) 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

3) 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

4) 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

5) 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

6) 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
HAL preprint hal-01784181

7) 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

8) 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

9) 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

10) 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

11) 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

12) 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

13) 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

14) 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

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
HAL preprint hal-01778044

16) 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

17) 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

18) 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

19) 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

20) 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

21) 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

22) 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

23) 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

24) 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

25) 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

26) 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

27) 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

28) 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

Proceedings (4)

1) 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

2) 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

3) 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

4) 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

Book chapters (3)

1) 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, 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

2) D. A. Di Pietro and R. Tittarelli
An introduction to Hybrid High-Order methods
in Numerical Methods for PDEs, 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

3) 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