A Stable Weak Galerkin Finite Element Method for Stokes Problem
This work addresses the need for stable finite element methods for Stokes problems, offering a simpler formulation that avoids additional stabilization terms.
The paper presents a new weak Galerkin finite element method for the Stokes problem that satisfies the discrete inf-sup condition without adding stability or penalty terms, and derives optimal error estimates for velocity and pressure approximations.
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.