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 three-dimensional polyhedral domains. More precisely, we shall analyze the convergence of the $hp$-IP dG methods considered in [33] which are based on $\sigma$-geometric anisotropic meshes and anisotropic polynomial degree distributions of $\mu$-bounded variation.