ANR HHOMM

<!-- <img src="HHOMM_Logo.png" width="120"/>--> Hybrid High-Order Methods on polyhedral Meshes
Title Hybrid High-Order Methods on polyhedral Meshes
Acronym HHOMM
Financing institution Agence Nationale de la Recherche
Reference ANR-15-CE40-0005
Challenge Société de l'information et de la communication
Axis Fondements du numérique
Principal investigator Daniele A. Di Pietro (DDP), Université de Montpellier
Participants Jérôme Droniou (JD), Monash University
Alexandre Ern (AE), Ecole des Ponts
Fabien Marche (FM), Université de Montpellier
Ruben Specogna (RS), Università di Udine
Call Appel à projets générique 2015
Financing mode JCJC
Starting date 1st November 2015

Publications

Books (1)

book   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 (27)

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
arXiv preprint arXiv:1707.04038

2) M. Botti, D. A. Di Pietro, and P. Sochala
A Hybrid High-Order discretisation method for nonlinear poroelasticity
Comput. Meth. Appl. Math., 2019. Published online. DOI: 10.1515/cmam-2018-0142
HAL preprint hal-01785810, arXiv preprint arXiv:1906.00757

3) 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

4) 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

5) 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

6) D. A. Di Pietro and J. Droniou
A third Strang lemma for schemes in fully discrete formulation
Calcolo, 2018, 55(40). DOI: 10.1007/s10092-018-0282-3
HAL preprint hal-01778044, arXiv preprint arXiv:1804.09484

7) 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

8) 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

9) 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

10) 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

11) 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

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) 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

14) 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

15) 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

16) 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

17) 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

18) 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

19) 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

20) 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

21) 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

22) 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

23) 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. and Math. with Appl., 2017, 73(7):1593–1610. DOI: 10.1016/j.camwa.2017.02.005
HAL preprint hal-01366646

24) 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

25) 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

26) 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

27) 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
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

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
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

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. No 114 in Lecture Notes in Computational Science and Engineering
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 (0)

1) D. A. Di Pietro, J. Droniou, and F. Rapetti
Fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra
HAL preprint hal-02356810, arXiv preprint arXiv:1911.03616, November 2019
2) 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
HAL preprint hal-02151236, June 2019

Actions

18/4/2017 21/4/2017 Visit of L. Botti at IMAG
9/2/2017 18/2/2017 Visit of RT at Università di Udine
26/9/2016 28/9/2016 Visit at IMAG (JD)
20/6/2016 10/7/2016 Visit at Università di Bergamo (DDP)
1/7/2016 R. Tittarelli (RT) has joined the team as a post-doc researcher
12/5/2016 13/5/2016 Visit of M. Cicuttin at IMAG
1/3/2016 31/3/2016 Visit at IMAG (RS)
7/3/2016 18/3/2016 Visit of L. Botti at IMAG

Dissemination of the results

28/5/2018 1/6/2018 Invited presentation at CANUM, Cap d'Agde, France (DDP)
25/9/2017 29/9/2017 Two invited presentations at ENUMATH 2017, Voss, Norway (DDP, represented by M. Botti and RT)
22/7/2018 27/7/2018 Invited presentation at WCCMXIII, New York City (DDP, represented by M. Botti)
11/12/2017 13/12/2017 NumWave workshop at IMAG
19/12/2017 Invited seminar at Università di Bergamo (DDP)
13/11/2017 14/11/2017 Invited lecture at Journées Multiphasiques et Incertitudes, Nantes (DDP). Slides available here
17/7/2017 20/7/2017 Invited presentation at USNCCM14, Montréal (MC)
11/4/2017 Invited seminar at UMPA Lyon (DDP)
20/12/2016 Invited seminar at MOX, Politecnico di Milano (DDP)
29/9/2016 Invited seminar at LMGC (DDP)
13/9/2016 14/9/2016 Doctoral course on HHO methods within the thematic quarter NMPDEs at Institut Henri Poincaré (DDP). Slides available here
27/6/2016 1/7/2016 Invited talk on HHO methods at the ICOSAHOM conference in Rio de Janeiro (JD)
7/7/2016 Doctoral course on HHO methods at Università di Bergamo (DDP). Further details here
13/6/2016 17/6/2016 Two invited talks on HHO methods at the MAFELAP 2016 conference at Brunel University, London (DDP). Slides available here and here
5/6/2016 10/6/2016 One plenary talk (AE) and two invited talks (M. Botti and F. Chave) on HHO methods at the ECCOMAS 2016 conference in Crete
17/5/2016 18/5/2016 Invited lecture series at the Journées Numériques à Nice 2016 (DDP, AE). Practical sessions organized by L. Botti and M. Cicuttin

Updated 14/11/2019