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Analysis of a New NFV Scheme Preserving DMP for Two-Dimensional Sub-diffusion Equation on Distorted Meshes

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Abstract

In this paper, we describe a new nonlinear finite-volume scheme that preserves the discrete maximum principle (DMP) for the two-dimensional sub-diffusion equation on distorted meshes. One distinguishing feature of our method is its ability to uphold the DMP for the anisotropic sub-diffusion problems, thereby ensuring the absence of spurious oscillations in numerical solutions and maintaining the physical bounds of various quantities, such as concentration, temperature, and density. Notably, our scheme offers the advantage of being applicable to distorted meshes without stringent constraints. Numerical results demonstrate that our scheme successfully preserves maximum principle on various randomly distorted meshes.

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Acknowledgements

The authors are grateful for helpful suggestions from reviewers.

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Authors and Affiliations

  1. School of Science, Hunan University of Technology, Zhuzhou, 412007, China

    Xuehua Yang

  2. Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA

    Zhimin Zhang

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  1. Xuehua Yang
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The work was supported by National Natural Science Foundation of China Mathematics Tianyuan Foundation (12226340, 12226337).

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Yang, X., Zhang, Z. Analysis of a New NFV Scheme Preserving DMP for Two-Dimensional Sub-diffusion Equation on Distorted Meshes. J Sci Comput 99, 80 (2024). https://doi.org/10.1007/s10915-024-02511-7

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  • DOI: https://doi.org/10.1007/s10915-024-02511-7

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