Weak Galerkin finite element method for linear poroelasticity problems

2022/08/09 by Shanshan Gu, Gu, Shanshan, Shimin Chai +3 · 1 citation
Computer Science · Engineering · Mathematics · #65M15 #65M60 #76S05 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2208.04785

openalex publication_date 2022/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to a weak Galerkin (WG) finite element method for linear poroelasticity problems where weakly defined divergence and gradient operators over discontinuous functions are introduced. We establish both the continuous and discrete time WG schemes, and obtain their optimal convergence order estimates in a discrete H¹ norm for the displacement and in an H¹ type and L² norms for the pressure. Finally, numerical experiments are presented to illustrate the theoretical error results in different kinds of meshes which shows the WG flexibility for mesh selections, and to verify the locking-free property of our proposed method.

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• Sequential symmetric interior penalty discontinuous Galerkin method for fully coupled quasi-static thermo-poroelasticity problems

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