Abstract
A mixed finite element method is developed for a semilinear fourth-order elliptic boundary value problem. The existence and uniqueness of the solutions to the mixing problem are proved by constructing an auxiliary problem. Moreover, a computational format is provided for numerical calculation, the convergence of this problem is proved under some hypothetical conditions. The optimal error estimate of the semilinear fourth-order elliptic boundary value problem is analyzed by a two-grid method. Finally, some numerical examples are provided to support the theoretical analysis.
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Acknowledgements
This work is supported by the National Basic Research Program of China (Grant No. 2012CB025904). The authors would also like to thank all reviewers for their hard work and crucial suggestions, which improved the quality of this article.
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Communicated by Zhaosheng Feng.
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Song, S., Xie, S. A mixed element computing scheme for a semilinear fourth-order problem. Comp. Appl. Math. 40, 153 (2021). https://doi.org/10.1007/s40314-021-01545-z
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DOI: https://doi.org/10.1007/s40314-021-01545-z