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Optimal error estimates of the semidiscrete central discontinuous Galerkin methods for linear hyperbolic equations

Yong Liu Chi-Wang Shu Brown University Mengping Zhang

Numerical Analysis and Scientific Computing mathscidoc:1804.25025

SIAM Journal on Numerical Analysis, 56, 520-541, 2018
We analyze the central discontinuous Galerkin (DG) method for time-dependent linear conservation laws. In one dimension, optimal a priori $L^2$ error estimates of order $k+1$ are obtained for the semidiscrete scheme when piecewise polynomials of degree at most $k$ ($k\geq0$) are used on overlapping uniform meshes. %Our analysis is valid for both periodic boundary conditions and %for inflow-outflow boundary conditions. We then extend the analysis to multidimensions on uniform Cartesian meshes when piecewise tensor product polynomials are used on overlapping meshes. Numerical experiments are given to demonstrate the theoretical results.
Optimal error estimate; central DG; superconvergence points
[ Download ] [ 2018-04-16 10:53:34 uploaded by chiwangshu ] [ 625 downloads ] [ 0 comments ] 
@inproceedings{yong2018optimal,
  title={Optimal error estimates of the semidiscrete central discontinuous Galerkin methods for linear hyperbolic equations},
  author={Yong Liu, Chi-Wang Shu, and Mengping Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180416105334483040060},
  booktitle={SIAM Journal on Numerical Analysis},
  volume={56},
  pages={520-541},
  year={2018},
}
Yong Liu, Chi-Wang Shu, and Mengping Zhang. Optimal error estimates of the semidiscrete central discontinuous Galerkin methods for linear hyperbolic equations. 2018. Vol. 56. In SIAM Journal on Numerical Analysis. pp.520-541. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180416105334483040060.
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