A discontinuous Galerkin Method for parabolic problems with modified hp-finite element approximation technique

A recent paper [Hideaki Kaneko, Kim S. Bey, Gene J.W. Hou, Discontinuous Galerkin finite element method for parabolic problems, preprint November 2000, NASA] is generalized to a case where the spatial region is taken in R3. The region is assumed to be a thin body, such as a panel on the wing or fuselage of an aerospace vehicle. The traditional h- as well as hp-finite element methods are applied to the surface defined in the x-y variables, while, through the thickness, the technique of the p-element is employed. Time and spatial discretization scheme developed in Kaneko et al. (2000), based upon an assumption of certain weak singularity of ∥ut∥2, is used to derive an optimal a priori error estimate for the current method.