A stabilizer free WG Method for the Stokes Equations with order two superconvergence on polytopal mesh

TL;DR

This paper introduces a stabilizer-free weak Galerkin method for the Stokes equations that achieves superconvergence and optimal error estimates on polytopal meshes, demonstrated through comprehensive numerical tests.

Contribution

It presents a novel stabilizer-free weak Galerkin method with superconvergence properties and optimal error estimates for the Stokes equations on polytopal meshes.

Findings

Velocity approximation converges two orders faster than optimal.

Achieves optimal order pressure error estimates in L^2 norm.

Numerical examples confirm superconvergence in 2D and 3D cases.

Abstract

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 $L^2$ norm. Optimal order error estimate for pressure in the $L^2$ norm is also established. The numerical examples cover low and high order approximations, and 2D and 3D cases.