Exponential convergence of mixed hp-DGFEM for the incompressible Navier-Stokes equations in R²

Abstract

In a polygon Ω ⊂ R2, we consider mixed hp-discontinuous Galerkin approximations of the stationary, incompressible Navier-Stokes equations, subject to no-slip boundary conditions. We use geometrically corner-refined meshes and hp spaces with linearly increasing polynomial degrees. Based on recent results on analytic regularity of velocity field and pressure of Leray solutions in Ω, we prove exponential rates of convergence of the mixed hp-discontinuous Galerkin finite element method (hp-DGFEM), with respect to the number of degrees of freedom, for small data which is piecewise analytic