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Analysis of the nonlinear scheme preserving the maximum principle for the anisotropic diffusion equation on distorted meshes

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Abstract

In this paper, a nonlinear finite volume scheme preserving the discrete maximum principle for the anisotropic diffusion equation on distorted meshes is described. We prove the coercivity of the scheme under some constraints on the cell deformation and the diffusion coefficient. Numerical results show that the scheme is indeed coercive and satisfies the discrete maximum principle, and the accuracy of this scheme is remarkably better than that of an existing scheme preserving the discrete maximum principle on random triangular meshes.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 12071045 and 11971069), the Foundation of CAEP (China Academy of Engineering Physics) (Grant No. CX20210042) and the Foundation of LCP (Laboratory of Computational Physics).

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Authors and Affiliations

  1. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China

    Zhiqiang Sheng & Guangwei Yuan

  2. HEDPS, Center for Applied Physics and Technology, and College of Engineering, Peking University, Beijing, 100871, China

    Zhiqiang Sheng

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  1. Zhiqiang Sheng
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  2. Guangwei Yuan
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Correspondence to Guangwei Yuan.

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Sheng, Z., Yuan, G. Analysis of the nonlinear scheme preserving the maximum principle for the anisotropic diffusion equation on distorted meshes. Sci. China Math. 65, 2379–2396 (2022). https://doi.org/10.1007/s11425-021-1931-3

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  • DOI: https://doi.org/10.1007/s11425-021-1931-3

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