Abstract: We prove that the superconvergence properties of the hybridizable discontinuous Galerkin method for second-order elliptic problems do hold uniformly in time for the semidiscretization by the same method of the heat equation provided the solution is smooth enough. Thus, if the approximations are piecewise polynomials of degree , the approximation to the gradient converges with the rate for and the -projection of the error into a space of lower polynomial degree superconverges with the rate for uniformly in time. As a consequence, an element-by-element postprocessing converges with the rate for also uniformly in time. Similar results are proven for the Raviart-Thomas and the Brezzi-Douglas-Marini mixed methods.
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Brandon Chabaud Affiliation:
Department of Mathematics, Pennsylvania State University, University Park, State College, Pennsylvania 16802
Email:
chabaud@math.psu.edu
Bernardo Cockburn Affiliation:
School of Mathematics, University of Minnesota, 206 Church Street S.E., Minneapolis, Minnesota 55455
Email:
cockburn@math.umn.edu