Discontinuous Galerkin methods on hp-anisotropic meshes I: a priori error analysis

We consider the a priori error analysis of hp-version interior penalty discontinuous Galerkin methods for second–order partial differential equations with nonnegative characteristic form under weak assumptions on the mesh design and the local finite element spaces employed. In particular, we prove a priori hp-error bounds for linear target functionals of the solution, on (possibly) anisotropic computational meshes with anisotropic tensor-product polynomial basis functions. The theoretical results are illustrated by a numerical experiment.