A pressure-robust stabilizer-free WG finite element method for the Stokes equations on simplicial grids

A pressure-robust stabilizer-free weak Galerkin (WG) finite element method has been defined for the Stokes equations on triangular and tetrahedral meshes. We have obtained pressure-independent error estimates for the velocity without any velocity reconstruction. The optimal-order convergence for the velocity of the WG approximation has been proved for the $L^2$ norm and the $H^1$ norm. The optimal-order error convergence has been proved for the pressure in the $L^2$ norm. The theory has been validated by performing some numerical tests on triangular and tetrahedral meshes.