Priori Error Estimates for an HP-Version of the Discontinuous Galerkin Method forHyperbolic Conservation Laws

摘要

A priori error estimates are derived for hp-versions of the finite element methodfor discontinuous Galerkin approximations of a model class of linear, scalar, first-order hyperbolic conservation laws. These estimates are derived in a mesh dependent norm in which the coefficients depend upon both the local mesh size h(sub K) and a number p(sub k) which can be identified with the spectral order of the local approximations over each element.