Higher order space-time elements for a non-linear Biot model
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2019Metadata
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Lecture Notes in Computational Science and Engineering. 2019, 126, 541–549. https://doi.org/10.1007/978-3-319-96415-7_49Abstract
In this work, we consider a non-linear extension of the linear, quasi-static Biot’s model. Precisely, we assume that the volumetric strain and the fluid compressibility are non-linear functions. We propose a fully discrete numerical scheme for this model based on higher order space-time elements. We use mixed finite elements for the flow equation, (continuous) Galerkin finite elements for the mechanics and discontinuous Galerkin for the time discretization. We further use the L-scheme for linearising the system appearing on each time step. The stability of this approach is illustrated by a numerical experiment.