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Plane Wave Discontinuous Galerkin Methods: Exponential Convergence of the hp-version

by R. Hiptmair and A. Moiola and I. Perugia

(Report number 2013-31)

Abstract
We consider the two-dimensional Helmholtz equation with constant coefficients on a domain with piecewise analytic boundary, modelling the scattering of acoustic waves at a sound soft obstacle. Our discretisation relies on the Trefftz-discontinuous Galerkin approach with plane wave basis functions on meshes with very general element shapes, geometrically graded towards domain corners. We prove exponential convergence of the discrete solution in terms of number of unknowns.

Keywords: Helmholtz equation, sound-soft wave scattering, analytic regularity, Approximation by plane waves, Trefftz-discontinuous Galerkin method, hp-version, a priori convergence analysis, locally refined meshes, exponential convergence.

@Techreport{HMP13_528,
  author = {R. Hiptmair and A. Moiola and I. Perugia},
  title = {Plane Wave Discontinuous Galerkin Methods: Exponential Convergence of the hp-version},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2013-31},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2013/2013-31.pdf },
  year = {2013}
}

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