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

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 homogeneous Dirichlet boundary conditions and piecewise analytic data in three-dimensional polyhedral domains. More precisely, we shall analyze the convergence of the hp-IP dG methods considered in [33] based on axiparallel σ-geometric anisotropic meshes and anisotropic polynomial degree distributions of μ-bounded variation.