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Abstract: We derive energy-norm a posteriori error bounds for an Euler time-steppingmethod combined with various spatial discontinuous Galerkin schemes for linearparabolic problems. For accessibility, we address first the spatiallysemidiscrete case, and then move to the fully discrete scheme by introducingthe implicit Euler time-stepping. All results are presented in an abstractsetting and then illustrated with particular applications. This enables theerror bounds to hold for a variety of discontinuous Galerkin methods, providedthat energy-norm a posteriori error bounds for the corresponding ellipticproblem are available. To illustrate the method, we apply it to the interiorpenalty discontinuous Galerkin method, which requires the derivation of novel aposteriori error bounds. For the analysis of the time-dependent problems we usethe elliptic reconstruction technique and we deal with the nonconforming partof the error by deriving appropriate computable a posteriori bounds for it.



Autor: Emmanuil H. Georgoulis, Omar Lakkis, Juha M. Virtanen

Fuente: https://arxiv.org/







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