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arXiv · 2304.13365

Coupling nonconforming and enriched Galerkin methods for robust discretization and fast solvers of poroelasticity problems

Jeonghun J. Lee·Jacob Moore
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Abstract

In this paper we propose a new finite element discretization for the two-field formulation of poroelasticity which uses the elastic displacement and the pore pressure as primary variables. The main goal is to develop a numerical method with small problem sizes which still achieve key features such as parameter-robustness, local mass conservation, and robust preconditionor construction. For this we combine a nonconforming finite element and the interior over-stabilized enriched Galerkin methods with a suitable stabilization term. Robust a priori error estimates and parameter-robust preconditioner construction are proved, and numerical results illustrate our theoretical findings.

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Jeonghun J. Lee, Jacob Moore. 2023-04-26. Coupling nonconforming and enriched Galerkin methods for robust discretization and fast solvers of poroelasticity problems. https://arxiv.org/abs/2304.13365

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