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Local Analysis of Local Discontinuous Galerkin Method for the Time-Dependent Singularly Perturbed Problem

Yao Cheng Nanjing University Feng Zhang Nanjing University Qiang Zhang Nanjing University

Numerical Analysis and Scientific Computing mathscidoc:1702.25026

J Sci Comput, (63), 452-477, 2015.5
nthispaperwewillpresentthelocalstabilityanalysisandlocalerrorestimatefor the local discontinuous Galerkin (LDG) method, when solving the time-dependent singularly perturbed problems in one dimensional space with a stationary outflow boundary layer. Based on a general framework on the local stability, we obtain the optimal error estimate out of the local subdomain, which is nearby the outflow boundary point and has the width of O(h log(1/h)), for the semi-discrete LDG scheme and the fully-discrete LDG scheme with the second order explicit Runge–Kutta time-marching. Here h is the maximum mesh length. The numerical experiments are given also.
Local stability analysis · Local error estimate · Local discontinuous Galerkin method · Singularly perturbed · Outflow boundary layer
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@inproceedings{yao2015local,
  title={Local Analysis of Local Discontinuous Galerkin Method for the Time-Dependent Singularly Perturbed Problem},
  author={Yao Cheng, Feng Zhang, and Qiang Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208223326081947324},
  booktitle={J Sci Comput},
  number={63},
  pages={452-477},
  year={2015},
}
Yao Cheng, Feng Zhang, and Qiang Zhang. Local Analysis of Local Discontinuous Galerkin Method for the Time-Dependent Singularly Perturbed Problem. 2015. In J Sci Comput. pp.452-477. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208223326081947324.
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