hp-FEM for incompressible fluid flow - stable and stabilized

Abstract

The stable Galerkin formulation and a stabilized Galerkin Least Squares formulation for the Stokes problem are analyzed in the context of the hpversion of the Finite Element Method (FEM). Theoretical results for both formulations establish exponential rates of convergence and are confirmed by intensive numerical convergence studies. In our numerical experiments we demonstrate that these hp-FEM with geometric mesh refinement can resolve corner singularities at an exponential rate.