A Hybrid High-Order Discretization Method for Nonlinear Poroelasticity

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 discretize...

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Vydáno v:Journal of computational methods in applied mathematics Ročník 20; číslo 2; s. 227 - 249
Hlavní autoři: Botti, Michele, Di Pietro, Daniele A., Sochala, Pierre
Médium: Journal Article
Jazyk:angličtina
Vydáno: Minsk De Gruyter 01.04.2020
Walter de Gruyter GmbH
Témata:
65N08
65N30
76S05
Approximation
Compressible fluids
Discontinuous Galerkin Methods
Discretization
Formability
Galerkin method
Hybrid High-Order Methods
Korn’s Inequality
Methods
Nonlinear Biot Problem
Nonlinear Poroelasticity
Permeability
Polyhedral Meshes
Poroelasticity
Porous media
ISSN:1609-4840, 1609-9389
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Popis
Shrnutí: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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ISSN:1609-4840
1609-9389
DOI:10.1515/cmam-2018-0142