Multiscale stabilization for convection diffusion equations with heterogeneous velocity and diffusion coefficients

Tsz Shun Eric CHUNG Yalchin Efendiev Wing Tat Leung

Numerical Analysis and Scientific Computing mathscidoc:1910.43605

arXiv preprint arXiv:1807.11529, 2019.7
We present a new stabilization technique for multiscale convection diffusion problems. Stabilization for these problems has been a challenging task, especially for the case with high Peclet numbers. Our method is based on a constraint energy minimization idea and the discontinuous Petrov-Galerkin formulation. In particular, the test functions are constructed by minimizing an appropriate energy subject to certain orthogonality conditions, and are related to the trial space. The resulting test functions have a localization property, and can therefore be computed locally. We will prove the stability, and present several numerical results. Our numerical results confirm that our test space gives a good stability, in the sense that the solution error is close to the best approximation error.
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@inproceedings{tsz2019multiscale,
  title={Multiscale stabilization for convection diffusion equations with heterogeneous velocity and diffusion coefficients},
  author={Tsz Shun Eric CHUNG, Yalchin Efendiev, and Wing Tat Leung},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020203823238052134},
  booktitle={arXiv preprint arXiv:1807.11529},
  year={2019},
}
Tsz Shun Eric CHUNG, Yalchin Efendiev, and Wing Tat Leung. Multiscale stabilization for convection diffusion equations with heterogeneous velocity and diffusion coefficients. 2019. In arXiv preprint arXiv:1807.11529. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020203823238052134.
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