Energy conserving local discontinuous Galerkin methods for wave propagation problems

Yulong Xing University of Tennessee Ching-Shan Chou The Ohio State University Chi-Wang Shu Brown University

Numerical Analysis and Scientific Computing mathscidoc:1610.25058

Inverse Problems and Imaging, 7, 967-986, 2013
Wave propagation problems arise in a wide range of applications. The energy conserving property is one of the guiding principles for numerical algorithms, in order to minimize the phase or shape errors after long time integration. In this paper, we develop and analyze a local discontinuous Galerkin (LDG) method for solving the wave equation. We prove optimal error estimates, superconvergence toward a particular projection of the exact solution, and the energy conserving property for the semi-discrete formulation. The analysis is extended to the fully discrete LDG scheme, with the centered second-order time discretization (the leap-frog scheme). Our numerical experiments demonstrate optimal rates of convergence and superconvergence. We also show that the shape of the solution, after long time integration, is well preserved due to the energy conserving property.
wave propagation, local discontinuous Galerkin method, energy conservation, error estimate, superconvergence
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@inproceedings{yulong2013energy,
  title={Energy conserving local discontinuous Galerkin methods for wave propagation problems},
  author={Yulong Xing, Ching-Shan Chou, and Chi-Wang Shu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012061009693923176},
  booktitle={Inverse Problems and Imaging},
  volume={7},
  pages={967-986},
  year={2013},
}
Yulong Xing, Ching-Shan Chou, and Chi-Wang Shu. Energy conserving local discontinuous Galerkin methods for wave propagation problems. 2013. Vol. 7. In Inverse Problems and Imaging. pp.967-986. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012061009693923176.
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