A Stabilizer-Free, Pressure-Robust, and Superconvergence Weak Galerkin Finite Element Method for the Stokes Equations on Polytopal Mesh

In this paper, we propose a new stabilizer-free and pressure-robust weak Galerkin finite element method for the Stokes equations with superconvergence on polytopal mesh in primary velocity-pressure formulation. Convergence rates one order higher than optimal velocity both energy norm $L^2$-norm pressure are proved our proposed scheme. The $H$(div)-preserving operator has been constructed based polygonal arbitrary polynomial degrees employed body source assembling to break locking phenomenon induced by poor mass conservation classical discretization. Moreover, error scheme is be independent of thus confirm pressure-robustness. For simulation, only modifies but keeps same stiffness matrix. Four numerical experiments conducted validate convergence results robustness.