An Adaptive Discontinuous Galerkin Scheme for Second Order Problems with an Interface

P. Zunino ()
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P. Zunino: Politecnico di Milano, MOX – Department of Mathematics

A chapter in Numerical Mathematics and Advanced Applications, 2008, pp 397-404 from Springer

Abstract: Abstract We discuss the derivation of an a-posteriori local error indicator for a discontinuous Galerkin (DG) method based on weighted interior penalties applied to advection-diffusion-reaction equations featuring a diffusivity parameter that may be discontinuous along a planar interface on a two-dimensional domain. We demonstrate how the weights incorporate into the scheme some a-priori knowledge of the exact solution that improves the efficacy of the local error estimator and of the corresponding adapted mesh. All the theoretical results are illustrated and discussed by means of numerical experiments.

Keywords: Local Error; Discontinuous Galerkin Method; Order Problem; Interior Penalty; Local Error Indicator (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-69777-0_47

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DOI: 10.1007/978-3-540-69777-0_47

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