An Adaptive Staggered Discontinuous Galerkin Method for the Steady State ConvectionDiffusion Equation

Jie Du Tsz Shun Eric CHUNG

Numerical Analysis and Scientific Computing mathscidoc:1910.43557

Journal of Scientific Computing, 77, (3), 1490-1518, 2018.12
Staggered grid techniques have been applied successfully to many problems. A distinctive advantage is that physical laws arising from the corresponding partial differential equations are automatically preserved. Recently, a staggered discontinuous Galerkin (SDG) method was developed for the convectiondiffusion equation. In this paper, we are interested in solving the steady state convectiondiffusion equation with a small diffusion coefficient . It is known that the exact solution may have large gradient in some regions and thus a very fine mesh is needed. For convection dominated problems, that is, when is small, exact solutions may contain sharp layers. In these cases, adaptive mesh refinement is crucial in order to reduce the computational cost. In this paper, a new SDG method is proposed and the proof of its stability is provided. In order to construct an adaptive mesh refinement strategy for this new
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@inproceedings{jie2018an,
  title={An Adaptive Staggered Discontinuous Galerkin Method for the Steady State ConvectionDiffusion Equation},
  author={Jie Du, and Tsz Shun Eric CHUNG},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020202240828358086},
  booktitle={Journal of Scientific Computing},
  volume={77},
  number={3},
  pages={1490-1518},
  year={2018},
}
Jie Du, and Tsz Shun Eric CHUNG. An Adaptive Staggered Discontinuous Galerkin Method for the Steady State ConvectionDiffusion Equation. 2018. Vol. 77. In Journal of Scientific Computing. pp.1490-1518. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020202240828358086.
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