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A new family of expanded mixed finite element methods for reaction–diffusion equations

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Abstract

A new family of expanded mixed finite element methods is constructed for solving the reaction–diffusion equations. Compared with the traditional expanded mixed element methods, the new methods result into splitting systems and the coefficient matrixes are symmetric positive definite. The uniqueness and stability of the proposed algorithms are considered, and the corresponding error estimates are derived. Finally, some numerical examples are presented to verify the effectiveness of the proposed algorithms.

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Acknowledgements

This work was supported partially by the Major Scientific and Technological Projects of CNPC (ZD2019-183-008), the Natural Science Foundation of Shandong Province (ZR2019MA015) and the Fundamental Research Funds for the Central Universities (20CX05011A).

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Authors and Affiliations

  1. College of Science, China University of Petroleum, Qingdao, 266580, China

    Bingjie Ji, Jiansong Zhang, Yun Yu, Jun Liu & Hui Guo

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  1. Bingjie Ji
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  2. Jiansong Zhang
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  3. Yun Yu
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  4. Jun Liu
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  5. Hui Guo
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Correspondence to Jiansong Zhang.

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Ji, B., Zhang, J., Yu, Y. et al. A new family of expanded mixed finite element methods for reaction–diffusion equations. J. Appl. Math. Comput. 68, 2857–2875 (2022). https://doi.org/10.1007/s12190-021-01634-6

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