非线性时间分数阶四阶混合次扩散和扩散波动方程的混合有限元算法
Mixed Finite Element Algorithm for a Nonlinear Time-Fractional Fourth-Order Mixed Sub-Diffusion and Diffusion Wave Equation
摘要: 本文数值求解了一个二维非线性时间分数阶四阶混合次扩散和扩散波动方程，在时间方向上采用L1-CN格式，在空间上通过混合有限元方法进行离散，并且在此基础上，给出了它的全离散格式。最后针对该数值格式提供了算法过程和数值算例，以及详细的收敛结果。
Abstract: In this article, the two-dimensional nonlinear time-fractional fourth-order mixed sub-diffusion and diffusion wave equation is numerically solved, where L1-CN scheme is used in the time direction, and the mixed finite element method is applied in space. Further, the fully discrete scheme is provided. Finally, the algorithm process, numerical example, and detailed convergence results are provided for this numerical scheme.
文章引用：杨宁. 非线性时间分数阶四阶混合次扩散和扩散波动方程的混合有限元算法[J]. 应用数学进展, 2024, 13(4): 1415-1424. https://doi.org/10.12677/aam.2024.134132

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