hp-dGFEM for Second-Order Elliptic Problems in Polyhedra II: Exponential Convergence

Abstract

The goal of this paper is to establish exponential convergence of hp-version interior penalty (IP) discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems with piecewise analytic data in threedimensional polyhedral domains. More precisely, we shall analyze the convergence of the hp-IP dG methods considered in [30] which are based on !-geometric anisotropic meshes of mapped hexahedra with "-uniform element mappings and anisotropic polynomial degree distributions of μ-bounded variation.