In this work, we introduce a novel algorithm for the Biot problem based on a hybrid high-order discretization of the mechanics and a symmetric weighted interior penalty discretization of the ow. The method has several assets, including, in particular, the support of general polyhedral meshes and arbitrary space approximation order. Our analysis delivers stability and error estimates that hold also when the specific storage coefficient vanishes, and shows that the constants have only a mild dependence on the heterogeneity of the permeability coefficient. Numerical tests demonstrating the performance of the method are provided.

A nonconforming high-order method for the Biot problem on general meshes

D Boffi;
2016

Abstract

In this work, we introduce a novel algorithm for the Biot problem based on a hybrid high-order discretization of the mechanics and a symmetric weighted interior penalty discretization of the ow. The method has several assets, including, in particular, the support of general polyhedral meshes and arbitrary space approximation order. Our analysis delivers stability and error estimates that hold also when the specific storage coefficient vanishes, and shows that the constants have only a mild dependence on the heterogeneity of the permeability coefficient. Numerical tests demonstrating the performance of the method are provided.
2016
Istituto di Matematica Applicata e Tecnologie Informatiche - IMATI -
Biot problem
Discontinuous Galerkin
General meshes
Hybrid high-order
Inf-sup stability
Poroelasticity
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Descrizione: A nonconforming high-order method for the Biot problem on general meshes
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.14243/332356
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