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Journal of Scientific Computing

, Volume 77, Issue 3, pp 1909–1935 | Cite as

Discontinuous Galerkin Methods for Acoustic Wave Propagation in Polygons

  • Fabian Müller
  • Dominik Schötzau
  • Christoph Schwab
Article
  • 111 Downloads

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.

Keywords

Linear wave equations Polygonal domains Corner singularities Discontinuous Galerkin finite element methods Mesh refinements Optimal convergence rates 

Mathematics Subject Classification

65M20 65M60 65N30 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Fabian Müller
    • 1
  • Dominik Schötzau
    • 2
  • Christoph Schwab
    • 1
  1. 1.Seminar for Applied MathematicsETH ZürichZurichSwitzerland
  2. 2.Mathematics DepartmentUniversity of British ColumbiaVancouverCanada

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