A Posteriori Error Bounds for Discontinuous Galerkin Methods for Quasilinear Parabolic Problems

Emmanuil H. Georgoulis () and Omar Lakkis ()
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Emmanuil H. Georgoulis: University of Leicester, Department of Mathematics
Omar Lakkis: University of Sussex, Department of Mathematics

A chapter in Numerical Mathematics and Advanced Applications 2009, 2010, pp 351-358 from Springer

Abstract: Abstract We derive a posteriori error bounds for a quasilinear parabolic problem, which is approximated by the hp-version interior penalty discontinuous Galerkin method (IPDG). The error is measured in the energy norm. The theory is developed for the semidiscrete case for simplicity, allowing to focus on the challenges of a posteriori error control of IPDG space-discretizations of strictly monotone quasilinear parabolic problems. The a posteriori bounds are derived using the elliptic reconstruction framework, utilizing available a posteriori error bounds for the corresponding steady-state elliptic problem.

Keywords: Posteriori Error; Discontinuous Galerkin; Discontinuous Galerkin Method; Posteriori Error Estimation; Interior Penalty (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-11795-4_37

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DOI: 10.1007/978-3-642-11795-4_37

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