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Mesh Conditions of the Preserving-Maximum-Principle Linear Finite Volume Element Method for Anisotropic Diffusion-Convection-Reaction Equations

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Abstract

We develop mesh conditions for linear finite volume element approximations of anisotropic diffusionconvectionreaction problems to satisfy the discrete maximum principle. We obtain the sufficient conditions to gurantee the both upper and lower bounds of the numerical solution when each angle of arbitrary triangle is \(\cal{O}(\Vert q\Vert_{\infty}h+\Vert g\Vert_{\infty}h^{2})\)-acute and h is small enough, where h denotes the mesh size, q and g are coefficients of the convection and reaction terms, respectively. To deal with the convection-dominated problems, we use the upwind triangle technique. For such scheme, the mesh condition can be sharper to \(\cal{O}(\Vert g\Vert_{\infty}h^{2})\)-acute. Some numerical examples are presented to demonstrate the theoretical results.

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Authors and Affiliations

  1. School of Mathematics, Jilin University, Changchun, 130012, China

    Lei Lin & Jun-liang Lv

  2. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Bei**g, 100088, China

    **g-yan Yue & Guang-wei Yuan

Authors
  1. Lei Lin
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  2. Jun-liang Lv
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  3. **g-yan Yue
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  4. Guang-wei Yuan
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Correspondence to Jun-liang Lv.

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The authors declare no conflict of interest.

The project is supported by the National Natural Science Foundation of China (No. 11301033, 11971069 and 12271209), the Natural Science Foundation of Jilin Province (No. 20200201259JC) and Jilin Province Science and Technology Plan Development Project (No. 20210201078GX).

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Lin, L., Lv, Jl., Yue, Jy. et al. Mesh Conditions of the Preserving-Maximum-Principle Linear Finite Volume Element Method for Anisotropic Diffusion-Convection-Reaction Equations. Acta Math. Appl. Sin. Engl. Ser. 39, 707–732 (2023). https://doi.org/10.1007/s10255-023-1060-9

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  • DOI: https://doi.org/10.1007/s10255-023-1060-9

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