Exponential convergence of hp-DGFEM for elliptic problems in polyhedral domains

Abstract

We review the recent results of [21, 22], and establish the exponential convergence of hp-version discontinuous Galerkin finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems with homogeneous Dirichlet boundary conditions and constant coefficients in threedimsional and axiparallel polyhedra. The exponential rates are confirmed in a series of numerical tests.