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

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.