Mathematics – Numerical Analysis
Scientific paper
2008-04-27
SIAM Journal on Numerical Analysis 2011 vol. 49 (2) pp. 427--458
Mathematics
Numerical Analysis
6 figures
Scientific paper
10.1137/080722461
We derive energy-norm a posteriori error bounds for an Euler time-stepping method combined with various spatial discontinuous Galerkin schemes for linear parabolic problems. For accessibility, we address first the spatially semidiscrete case, and then move to the fully discrete scheme by introducing the implicit Euler time-stepping. All results are presented in an abstract setting and then illustrated with particular applications. This enables the error bounds to hold for a variety of discontinuous Galerkin methods, provided that energy-norm a posteriori error bounds for the corresponding elliptic problem are available. To illustrate the method, we apply it to the interior penalty discontinuous Galerkin method, which requires the derivation of novel a posteriori error bounds. For the analysis of the time-dependent problems we use the elliptic reconstruction technique and we deal with the nonconforming part of the error by deriving appropriate computable a posteriori bounds for it.
Georgoulis Emmanuil H.
Lakkis Omar
Virtanen Juha M.
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