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A symmetric mixed covolume method for the nonlinear parabolic problem

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Abstract

In this paper, we develop a symmetric mixed covolume scheme for the nonlinear parabolic equations. The existence and uniqueness of the scheme are proved by using the lowest order Raviart–Thomas mixed element space on rectangular grids. We carry out a rigorous error estimates for the constructed scheme, establishing the first-order convergence for both velocity and pressure. Numerical examples are provided to verify that the numerical results are all in consistent with the theoretical analysis.

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Acknowledgements

This work is supported by Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, by China Postdoctoral Science Foundation under Grant Number 2020M672111, by National Natural Science Foundation of China under Grant Number 11931003, by the Shandong Provincial Science and Technology Development Program (2018GGX101036).

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, China

    Xuan Zhao

  2. Hunan Key Laboratory for Computation and Simulation in Science and Engineering and School of Mathematics and Computational Science, Xiangtan, China

    Zhengguang Liu

  3. School of Mathematics and Statistics, Shandong Normal University, Jinan, China

    Zhengguang Liu

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  1. Xuan Zhao
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  2. Zhengguang Liu
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Correspondence to Xuan Zhao.

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Zhao, X., Liu, Z. A symmetric mixed covolume method for the nonlinear parabolic problem. J. Appl. Math. Comput. 68, 1591–1611 (2022). https://doi.org/10.1007/s12190-021-01582-1

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  • DOI: https://doi.org/10.1007/s12190-021-01582-1

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