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Discontinuous Galerkin methods with staggered hybridization for linear elastodynamics

Eric T. Chung Department of Mathematics, The Chinese University of Hong Kong, Hong Kong Special Administrative Region Jie Du Department of Mathematics, The Chinese University of Hong Kong, Hong Kong Special Administrative Region Chi Yeung Lam Department of Mathematics, The Chinese University of Hong Kong, Hong Kong Special Administrative Region

TBD mathscidoc:2205.43004

Computers & Mathematics with Applications, 74, (6), 1198-1214, 2017.9
In this paper, we will develop a new staggered hybridization technique for discontinuous Galerkin methods to discretize linear elastodynamic equations. The idea of hybridization is used extensively in many discontinuous Galerkin methods, but the idea of staggered hybridization is new. Our new approach offers several advantages, namely energy conservation, high-order optimal convergence, preservation of symmetry for the stress tensor, block diagonal mass matrices as well as low dispersion error. The key idea is to use two staggered hybrid variables to enforce the continuity of the velocity and the continuity of the normal component of the stress tensor on a staggered mesh. We prove the stability and the convergence of the proposed scheme in both the semi-discrete and the fully-discrete settings. Numerical results confirm the optimal rate of convergence and show that the method has a superconvergent property for dispersion. Furthermore, an application of this method to Rayleigh wave propagation is presented.
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@inproceedings{eric2017discontinuous,
  title={Discontinuous Galerkin methods with staggered hybridization for linear elastodynamics},
  author={Eric T. Chung, Jie Du, and Chi Yeung Lam},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220520152019688630309},
  booktitle={Computers & Mathematics with Applications},
  volume={74},
  number={6},
  pages={1198-1214},
  year={2017},
}
Eric T. Chung, Jie Du, and Chi Yeung Lam. Discontinuous Galerkin methods with staggered hybridization for linear elastodynamics. 2017. Vol. 74. In Computers & Mathematics with Applications. pp.1198-1214. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220520152019688630309.
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