Weak Galerkin finite element method for linear poroelasticity problems

TL;DR

This paper introduces a weak Galerkin finite element method for linear poroelasticity problems, providing optimal convergence estimates and demonstrating flexibility and locking-free properties through numerical experiments.

Contribution

The paper develops a novel weak Galerkin finite element approach for linear poroelasticity, with proven optimal convergence and mesh flexibility.

Findings

Optimal convergence in discrete norms for displacement and pressure.

Method is locking-free and adaptable to various mesh types.

Numerical results confirm theoretical error estimates.

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 $H^1$ norm for the displacement and in an $H^1$ type and $L^2$ 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.