Robust weak Galerkin finite element solvers for Stokes flow based on a lifting operator

Abstract

This paper presents novel finite element solvers for Stokes flow that are pressure-robust due to the use of a lifting operator. Specifically, weak Galerkin (WG) finite element schemes are developed for the Stokes problem on quadrilateral and hexahedral meshes. Local Arbogast-Correa or Arbogast-Tao spaces are utilized for construction of discrete weak gradients. The lifting operator lifts WG test functions into H ( div ) -subspaces and removes pressure dependence of velocity errors. The pressure robustness of these solvers is validated theoretically and illustrated numerically. Comparison with the non-robust classical Taylor-Hood ( Q 2 , Q 1 ) solver is presented.