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A high order accurate bound-preserving compact finite difference scheme for scalar convection diffusion equations

Hao Li Purdue University Shusen Xie Ocean University of China Xiangxiong Zhang Purdue University

Numerical Analysis and Scientific Computing mathscidoc:1904.25014

SIAM Journal on Numerical Analysis, 56, (6), 3308-3345, 2018
We show that the classical fourth order accurate compact finite difference scheme with high order strong stability preserving time discretizations for convection diffusion problems satisfies a weak monotonicity property, which implies that a simple limiter can enforce the bound- preserving property without losing conservation and high order accuracy. Higher order accurate compact finite difference schemes satisfying the weak monotonicity will also be discussed.
finite difference method, compact finite difference, high order accuracy, convection diffusion equations, bound-preserving, maximum principle
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@inproceedings{hao2018a,
  title={ A high order accurate bound-preserving compact finite difference scheme for scalar convection diffusion equations},
  author={Hao Li, Shusen Xie, and Xiangxiong Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190430212711792886309},
  booktitle={SIAM Journal on Numerical Analysis},
  volume={56},
  number={6},
  pages={3308-3345},
  year={2018},
}
Hao Li, Shusen Xie, and Xiangxiong Zhang. A high order accurate bound-preserving compact finite difference scheme for scalar convection diffusion equations. 2018. Vol. 56. In SIAM Journal on Numerical Analysis. pp.3308-3345. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190430212711792886309.
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