A Two-Field Finite Element Solver For Poroelasticity On Quadrilateral Meshes

This paper presents a finite element solver for linear poroelasticity problems on quadrilateral meshes based on the displacement-pressure two-field model. This new solver combines the Bernardi-Raugel element for linear elasticity and a weak Galerkin element for Darcy flow through the implicit Euler temporal discretization. The solver does not use any penalty factor and has less degrees of freedom compared to other existing methods. The solver is free of nonphysical pressure oscillations, as demonstrated by numerical experiments on two widely tested benchmarks. Extension to other types of meshes in 2-dim and 3-dim is also discussed.