Inf-sup stable discretization of the quasi-static Biot's equations in poroelasticity
C Kreuzer, P Zanotti - arXiv preprint arXiv:2407.02939, 2024 - arxiv.org
C Kreuzer, P Zanotti
arXiv preprint arXiv:2407.02939, 2024•arxiv.orgWe propose a new full discretization of the Biot's equations in poroelasticity. The
construction is driven by the inf-sup theory, which we recently developed. It builds upon the
four-field formulation of the equations obtained by introducing the total pressure and the total
fluid content. We discretize in space with Lagrange finite elements and in time with
backward Euler. We establish inf-sup stability and quasi-optimality of the proposed
discretization, with robust constants with respect to all material parameters. We further …
construction is driven by the inf-sup theory, which we recently developed. It builds upon the
four-field formulation of the equations obtained by introducing the total pressure and the total
fluid content. We discretize in space with Lagrange finite elements and in time with
backward Euler. We establish inf-sup stability and quasi-optimality of the proposed
discretization, with robust constants with respect to all material parameters. We further …
We propose a new full discretization of the Biot's equations in poroelasticity. The construction is driven by the inf-sup theory, which we recently developed. It builds upon the four-field formulation of the equations obtained by introducing the total pressure and the total fluid content. We discretize in space with Lagrange finite elements and in time with backward Euler. We establish inf-sup stability and quasi-optimality of the proposed discretization, with robust constants with respect to all material parameters. We further construct an interpolant showing how the error decays for smooth solutions.
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