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Multiscale tailored finite point method for second order elliptic equations with rough or highly oscillatory coefficients

Houde Han Zhiwen Zhang

Numerical Analysis and Scientific Computing mathscidoc:1912.431041

Communications in Mathematical Sciences, 10, (3), 945-976, 2012.9
We develop a multiscale tailored finite point method (MsTFPM) for second order elliptic equations with rough or highly oscillatory coefficients. The finite point method has been tailored to some particular properties of the problem, so that it can capture the multiscale solutions using coarse meshes without resolving the fine scale structure of the solution. Several numerical examples in one-and two-dimensions are provided to show the accuracy and convergence of the proposed method. In addition, some analysis results based on the maximum principle for the one-dimensional problem are proved.
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@inproceedings{houde2012multiscale,
  title={Multiscale tailored finite point method for second order elliptic equations with rough or highly oscillatory coefficients},
  author={Houde Han, and Zhiwen Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211424437239605},
  booktitle={Communications in Mathematical Sciences},
  volume={10},
  number={3},
  pages={945-976},
  year={2012},
}
Houde Han, and Zhiwen Zhang. Multiscale tailored finite point method for second order elliptic equations with rough or highly oscillatory coefficients. 2012. Vol. 10. In Communications in Mathematical Sciences. pp.945-976. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211424437239605.
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