BDM H(div) weak Galerkin finite element methods for Stokes equations

Abstract

We add new inter-element variables to the BDM H(div) finite elements on triangular and tetrahedral meshes for the Stokes equations. With the weak gradient, we enforce weakly the tangential continuity of H(div) finite element velocity fields while not relaxing the normal continuity. The new method produces divergence-free H(div) finite element solutions of optimal-order convergence. Numerical examples are provided, confirming the theory and in particular, the pressure-robustness of the method.