A new modified weak Galerkin finite element scheme for solving the stationary Stokes equations

Abstract In this paper, a modified weak Galerkin method is proposed for the Stokes problem. The numerical scheme is based on a novel variational form of the Stokes problem. The degree of freedoms in the modified weak Galerkin method is less than that in the original weak Galerkin method, while the accuracy stays the same. In this paper, the optimal convergence orders are given and some numerical experiments are presented to verify the theory.