Abstract
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 R 3. 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 ∥ u t ∥ 2, is used to derive an optimal a priori error estimate for the current method.
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