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An adaptive SDG method for the Stokes system

Eric T. Chung Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, SAR, People’s Republic of China Jie Du Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, SAR, People’s Republic of China Man Chun Yuen Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, SAR, People’s Republic of China

Numerical Analysis and Scientific Computing mathscidoc:2205.25019

Journal of Scientific Computing, 70, 766-792, 2016.8
Staggered grid techniques are attractive ideas for flow problems due to their more enhanced conservation properties. Recently, a staggered discontinuous Galerkin method is developed for the Stokes system. This method has several distinctive advantages, namely high order optimal convergence as well as local and global conservation properties. In addition, a local postprocessing technique is developed, and the postprocessed velocity is superconvergent and pointwisely divergence-free. Thus, the staggered discontinuous Galerkin method provides a convincing alternative to existing schemes. For problems with corner singularities and flows in porous media, adaptive mesh refinement is crucial in order to reduce the computational cost. In this paper, we will derive a computable error indicator for the staggered discontinuous Galerkin method and prove that this indicator is both efficient and reliable. Moreover, we will present some numerical results with corner singularities and flows in porous media to show that the proposed error indicator gives a good performance.
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@inproceedings{eric2016an,
  title={An adaptive SDG method for the Stokes system},
  author={Eric T. Chung, Jie Du, and Man Chun Yuen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220520151354115989307},
  booktitle={Journal of Scientific Computing},
  volume={70},
  pages={766-792},
  year={2016},
}
Eric T. Chung, Jie Du, and Man Chun Yuen. An adaptive SDG method for the Stokes system. 2016. Vol. 70. In Journal of Scientific Computing. pp.766-792. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220520151354115989307.
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