A modified weak Galerkin finite element method for the Stokes equations

Abstract

A modified weak Galerkin (MWG) finite element method is introduced for the Stokes equations in the primary velocity–pressure formulation. This method is based on the weak Galerkin (WG) finite element method developed recently in Wang and Ye (0000). The unknowns associated with element boundaries in the WG method have been eliminated in the MWG method. As the result, the MWG method has fewer degrees of freedom. Optimal-order error estimates are established for the corresponding numerical approximation in various norms. Numerical results are presented to confirm the theory.