Analysis of a Hybrid High-Order–discontinuous Galerkin discretization method for nonlinear poroelasticity

Abstract : 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.
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Pré-publication, Document de travail
2018
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https://hal.archives-ouvertes.fr/hal-01785810
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  • HAL Id : hal-01785810, version 1

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Michele Botti, Daniele Antonio Di Pietro, Pierre Sochala. Analysis of a Hybrid High-Order–discontinuous Galerkin discretization method for nonlinear poroelasticity. 2018. 〈hal-01785810〉

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