Inf-Sup stable discretization of the quasi-static Biot's equations in poroelasticity

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dc.date.accessioned2024-08-06T11:19:38Z
dc.date.available2024-08-06T11:19:38Z
dc.date.issued2024-07
dc.description.abstractWe 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.en
dc.identifier.issn2190-1767
dc.identifier.urihttp://hdl.handle.net/2003/42636
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-24472
dc.language.isoen
dc.relation.ispartofseriesErgebnisberichte des Instituts für Angewandte Mathematik;675
dc.subjectInf-sup stabilityen
dc.subjectrobustnessen
dc.subjectquasioptimalityen
dc.subjectporoelasticityen
dc.subjectquasi-static Biot’s equationsen
dc.subjecta priori analysisen
dc.subject.ddc610
dc.titleInf-Sup stable discretization of the quasi-static Biot's equations in poroelasticityen
dc.typeText
dc.type.publicationtypePreprint
dcterms.accessRightsopen access
eldorado.secondarypublicationfalse

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