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A priori error estimates for semi-discrete discontinuous Galerkin methods solving nonlinear Hamilton-Jacobi equations with smooth solutions

Tao Xiong University of Science and Technology of China Chi-Wang Shu Brown University Mengping Zhang University of Science and Technology of China

Numerical Analysis and Scientific Computing mathscidoc:1610.25063

International Journal of Numerical Analysis and Modeling, 10, 154-177, 2013
In this paper, we provide a priori $L^2$ error estimates for the semi-discrete discontinuous Galerkin method and the local discontinuous Galerkin method for one- and two-dimensional nonlinear Hamilton-Jacobi equations with smooth solutions. With a special Gauss-Radau projection, the optimal error estimates on rectangular meshes are obtained.
Hamilton-Jacobi equations, discontinuous Galerkin method, local discontinuous Galerkin method, a priori error estimates
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@inproceedings{tao2013a,
  title={A priori error estimates for semi-discrete discontinuous Galerkin methods solving nonlinear Hamilton-Jacobi equations with smooth solutions},
  author={Tao Xiong, Chi-Wang Shu, and Mengping Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012101818906280181},
  booktitle={International Journal of Numerical Analysis and Modeling},
  volume={10},
  pages={154-177},
  year={2013},
}
Tao Xiong, Chi-Wang Shu, and Mengping Zhang. A priori error estimates for semi-discrete discontinuous Galerkin methods solving nonlinear Hamilton-Jacobi equations with smooth solutions. 2013. Vol. 10. In International Journal of Numerical Analysis and Modeling. pp.154-177. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012101818906280181.
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