Generalized weak Galerkin methods for Stokes equations

A finite element method, called generalized Weak Galerkin (gWG), is introduced for the Stokes equation by using a new weak gradient notion in usual approach. The gWG method allows polynomial elements of arbitrary order any combination velocity variable, but with proper constraints on pressure due to inf-sup condition. Error estimates are derived approximation mesh-dependent energy norm, as well L2 norm both and approximations. Some numerical examples presented verify accuracy, theoretical convergence order, robustness proposed scheme.