A phase-based interior penalty discontinuous Galerkin method for the Helmholtz equation with spatially varying wavenumber

Chi Yeung Lam Chi-Wang Shu Brown University

Numerical Analysis and Scientific Computing mathscidoc:1804.25006

Computer Methods in Applied Mechanics and Engineering, 318, 456-473, 2017
This paper is concerned with an interior penalty discontinuous Galerkin (IPDG) method based on a flexible type of non-polynomial local approximation space for the Helmholtz equation with varying wavenumber. The local approximation space consists of multiple polynomial-modulated phase functions which can be chosen according to the phase information of the solution. We obtain some {approximation} properties for this space and \textit{a prior} $L^2$ error estimates for the \textit{h}-convergence of the IPDG method using duality argument. We also provide ample numerical examples to show that, building phase information into the local spaces often gives more accurate results comparing to using the standard polynomial spaces.
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@inproceedings{chi2017a,
  title={A phase-based interior penalty discontinuous Galerkin method for the Helmholtz equation with spatially varying wavenumber},
  author={Chi Yeung Lam, and Chi-Wang Shu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180416093113380488041},
  booktitle={Computer Methods in Applied Mechanics and Engineering},
  volume={318},
  pages={456-473},
  year={2017},
}
Chi Yeung Lam, and Chi-Wang Shu. A phase-based interior penalty discontinuous Galerkin method for the Helmholtz equation with spatially varying wavenumber. 2017. Vol. 318. In Computer Methods in Applied Mechanics and Engineering. pp.456-473. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180416093113380488041.
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