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Journal of Scientific Computing

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06-04-2018

Discontinuous Galerkin Methods for Acoustic Wave Propagation in Polygons

Authors: Fabian Müller, Dominik Schötzau, Christoph Schwab

Published in: Journal of Scientific Computing | Issue 3/2018

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Abstract

We analyze space semi-discretizations of linear, second-order wave equations by discontinuous Galerkin methods in polygonal domains where solutions exhibit singular behavior near corners. To resolve these singularities, we consider two families of locally refined meshes: graded meshes and bisection refinement meshes. We prove that for appropriately chosen refinement parameters, optimal asymptotic rates of convergence with respect to the total number of degrees of freedom are obtained, both in the energy norm errors and the \(\mathcal {L}^2\)-norm errors. The theoretical convergence orders are confirmed in a series of numerical experiments which also indicate that analogous results hold for incompatible data which is not covered by the currently available regularity theory.

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Title: Discontinuous Galerkin Methods for Acoustic Wave Propagation in Polygons
Authors: Fabian Müller
Dominik Schötzau
Christoph Schwab
Publication date: 06-04-2018
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 3/2018
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-018-0706-x

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