Staggered discontinuous Galerkin methods for the Helmholtz equations with large wave number

Lina Zhao Eun-Jae Park Tsz Shun Eric CHUNG

Numerical Analysis and Scientific Computing mathscidoc:1910.43594

arXiv preprint arXiv:1904.12091, 2019.4
In this paper we investigate staggered discontinuous Galerkin method for the Helmholtz equation with large wave number on general quadrilateral and polygonal meshes. The method is highly flexible by allowing rough grids such as the trapezoidal grids and highly distorted grids, and at the same time, is numerical flux free. Furthermore, it allows hanging nodes, which can be simply treated as additional vertices. By exploiting a modified duality argument, the stability and convergence can be proved under the condition that \kappa h is sufficiently small, where \kappa h is the wave number and \kappa h is the mesh size. Error estimates for both the scalar and vector variables in \kappa h norm are established. Several numerical experiments are tested to verify our theoretical results and to present the capability of our method for capturing singular solutions.
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@inproceedings{lina2019staggered,
  title={Staggered discontinuous Galerkin methods for the Helmholtz equations with large wave number},
  author={Lina Zhao, Eun-Jae Park, and Tsz Shun Eric CHUNG},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020203454171225123},
  booktitle={arXiv preprint arXiv:1904.12091},
  year={2019},
}
Lina Zhao, Eun-Jae Park, and Tsz Shun Eric CHUNG. Staggered discontinuous Galerkin methods for the Helmholtz equations with large wave number. 2019. In arXiv preprint arXiv:1904.12091. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020203454171225123.
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