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Computational Methods in Applied Mathematics

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A Hybrid High-Order Discretization Method for Nonlinear Poroelasticity

Michele BottiORCID iD: https://orcid.org/0000-0003-1171-2874 / Daniele A. Di PietroORCID iD: https://orcid.org/0000-0003-0959-8830 / Pierre Sochala
Published Online: 2019-06-19 | DOI: https://doi.org/10.1515/cmam-2018-0142


In this work, we construct and analyze a nonconforming high-order discretization method for the quasi-static single-phase nonlinear poroelasticity problem describing Darcean flow in a deformable porous medium saturated by a slightly compressible fluid. The nonlinear elasticity operator is discretized using a Hybrid High-Order method, while the Darcy operator relies on a Symmetric Weighted Interior Penalty discontinuous Galerkin scheme. The method is valid in two and three space dimensions, delivers an inf-sup stable discretization on general meshes including polyhedral elements and nonmatching interfaces, supports arbitrary approximation orders, and has a reduced cost thanks to the possibility of statically condensing a large subset of the unknowns for linearized versions of the problem. Moreover, the proposed construction can handle both nonzero and vanishing specific storage coefficients.

Keywords: Nonlinear Poroelasticity; Nonlinear Biot Problem; Korn’s Inequality; Hybrid High-Order Methods; Discontinuous Galerkin Methods; Polyhedral Meshes

MSC 2010: 65N08; 65N30; 76S05


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About the article

Received: 2018-05-07

Revised: 2019-05-24

Accepted: 2019-05-31

Published Online: 2019-06-19

Funding Source: Agence Nationale de la Recherche

Award identifier / Grant number: ANR-10-LABX-20

Award identifier / Grant number: ANR-15-CE40-0005

This work was partially funded by the Bureau de Recherches Géologiques et Minières. The work of M. Botti was additionally partially supported by Labex NUMEV (ANR-10-LABX-20) ref. 2014-2-006. The work of D. A. Di Pietro was additionally partially supported by project HHOMM (ANR-15-CE40-0005).

Citation Information: Computational Methods in Applied Mathematics, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2018-0142.

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