Structure preserving approximation of dynamic poroelasticity
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Understanding the dynamics of flow in deformable porous media is an ongoing field of research in engineering and natural sciences. Here we present a holistic framework for analysis and approximation of systems of dynamic poroelasticity. The coupled hyperbolic-parabolic equations are rewritten as a first-order system in space and time. Discretizations by discontinuous Galerkin (DG) space-time finite element methods (STFEMs) are proposed and investigated. The numerical performance of the STFEMs and algebraic solver for the coupled hyperbolic- parabolic system is reviewed carefully. Second-order in space formulations (displacement-pressure form) are further encountered. A challenging three-dimensional test setting related to biomedical engineering is studied.
