Analysis of a 2-field finite element solver for poroelasticity on quadrilateral meshes

• Published in: Journal of computational and applied mathematics Vol. 393; p. 113539
• Main Authors: Wang, Zhuoran, Tavener, Simon, Liu, Jiangguo
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.09.2021
• Subjects: Arbogast–Correa spaces; Enriched Lagrangian finite elements; Poroelasticity; Quadrilateral meshes; Weak Galerkin; Enriched Lagrangian finite elements; Quadrilateral meshes; Weak Galerkin; Arbogast–Correa spaces; Poroelasticity
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2021.113539

This paper presents a novel 2-field finite element solver for linear poroelasticity on convex quadrilateral meshes. The Darcy flow is discretized for fluid pressure by a lowest-order weak Galerkin (WG) finite element method, which establishes the discrete weak gradient and numerical velocity in the lowest-order Arbogast–Correa space. The linear elasticity is discretized for solid displacement by the enriched Lagrangian finite elements with a special treatment for the volumetric dilation. These two types of finite elements are coupled through the implicit Euler temporal discretization to solve poroelasticity problems. A rigorous error analysis is presented along with numerical tests to demonstrate the accuracy and locking-free property of this new solver. •A FE solver for poroelasticity that solves for the two primal variables.•The solver uses the least degrees of freedom, compared to other existing methods.•The solver is locking-free.•Well-organized and easy-to-understand rigorous analysis.