Iterative Coupling of Variational Space-Time Methods for Biot’s System of Poroelasticity
In this work we present an iterative coupling scheme for the quasi-static Biot system of poroelasticity. For the discretization of the subproblems describing mechanical deformation and single-phase flow space-time finite element methods based on a discontinuous Galerkin approximation of the time variable are used. The spatial approximation of the flow problem is done by mixed finite element methods. The stability of the approach is illustrated by numerical experiments. The presented variational space-time framework is of higher order accuracy such that problems with high fluctuations become feasible. Moreover, it offers promising potential for the simulation of the fully dynamic Biot–Allard system coupling an elastic wave equation for solid’s deformation with single-phase flow for fluid infiltration.
KeywordsMixed Finite Element Finite Element Space Mixed Finite Element Method Fixed Point Iteration Time Discretization Scheme
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