A Stable Weak Galerkin Finite Element Method for Stokes Problem

TL;DR

This paper introduces a new stable weak Galerkin finite element method for the Stokes problem, providing optimal error estimates and confirming stability through numerical experiments.

Contribution

A novel weak Galerkin finite element space pair for Stokes problems that satisfies the inf-sup condition without additional stabilization.

Findings

Stable weak Galerkin scheme without penalty terms

Optimal error estimates for velocity and pressure

Numerical results confirm theoretical stability and accuracy

Abstract

We study the weak Galerkin finite element method for Stokes problem. A new weak Galerkin finite element velocity-pressure space pair is presented which satisfies the discrete inf-sup condition. Based on this space pair, we establish a stable weak Galerkin approximation scheme without adding any stability term or penalty term. Then, we further derive the optimal error estimates for velocity and pressure approximations, respectively. Numerical experiments are provided to illustrate the theoretical analysis.