A Hybridized Weak Galerkin Finite Element Method for Incompressible Stokes Equations

Abstract

In this paper, a hybridized weak Galerkin (HWG) finite element method is proposed for solving incompressible Stokes equations. The finite element space of the proposed method is constructed simply by piecewise polynomials. The optimal convergence order can be achieved for velocity function both in $L^2$ norm and $H^1$ norm, pressure function in $H^1$ norm. Finally, a Schur complement is employed to reduce the degree of freedom in discrete problem. Numerical examples are presented to demonstrate the effectiveness of the hybridized weak Galerkin finite element method.