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Journal Articles Computational Methods in Applied Mathematics Year : 2020

A Hybrid High-Order Discretization Method for Nonlinear Poroelasticity

Abstract

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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Dates and versions

hal-03710373 , version 1 (05-12-2022)

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Michele Botti, Daniele Di Pietro, Pierre Sochala. A Hybrid High-Order Discretization Method for Nonlinear Poroelasticity. Computational Methods in Applied Mathematics, 2020, 20 (2), pp.227-249. ⟨10.1515/cmam-2018-0142⟩. ⟨hal-03710373⟩
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