A stabilizer free WG method for the Stokes equations with order two superconvergence on polytopal mesh

Abstract

<p style='text-indent:20px;'>A stabilizer free WG method is introduced for the Stokes equations with superconvergence on polytopal mesh in primary velocity-pressure formulation. Convergence rates two order higher than the optimal-order for velocity of the WG approximation is proved in both an energy norm and the <inline-formula><tex-math id="M1">\begin{document}$ L^2 $\end{document}</tex-math></inline-formula> norm. Optimal order error estimate for pressure in the <inline-formula><tex-math id="M2">\begin{document}$ L^2 $\end{document}</tex-math></inline-formula> norm is also established. The numerical examples cover low and high order approximations, and 2D and 3D cases.</p>