A posteriori error estimation for hp-version time-stepping methods for parabolic partial differential equations
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- Schötzau, D. & Wihler, T.P. Numer. Math. (2010) 115: 475. doi:10.1007/s00211-009-0285-8
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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.