Chapter

Domain Decomposition Methods in Science and Engineering XVIII

Volume 70 of the series Lecture Notes in Computational Science and Engineering pp 51-62

Date:

Mixed Plane Wave Discontinuous Galerkin Methods

  • Ralf HiptmairAffiliated withSAM, ETH Zurich Email author 
  • , Ilaria PerugiaAffiliated withDipartimento di Matematica, Università di Pavia

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Summary

In this paper, we extend the class of plane wave discontinuous Galerkin methods for the two-dimensional inhomogeneous Helmholtz equation presented in Gittelson, Hiptmair, and Perugia [2007]. More precisely, we consider the case of numerical fluxes defined in mixed form, namely, numerical fluxes explicitly defined in terms of both the primal and the flux variable, instead of the primal variable and its gradient. In our error analysis, we rely heavily on the approximation results and inverse estimates for plane waves proved in Gittelson, Hiptmair, and Perugia [2007] and develop a new mixed duality argument.