, Volume 115, Issue 3, pp 475-509
Date: 13 Jan 2010

A posteriori error estimation for hp-version time-stepping methods for parabolic partial differential equations

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Abstract

The aim of this paper is to develop an hp-version a posteriori error analysis for the time discretization of parabolic problems by the continuous Galerkin (cG) and the discontinuous Galerkin (dG) time-stepping methods, respectively. The resulting error estimators are fully explicit with respect to the local time-steps and approximation orders. Their performance within an hp-adaptive refinement procedure is illustrated with a series of numerical experiments.

D. Schötzau was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC).