石东洋, 位一凡. Allen-Cahn方程的非协调元二重网格方法的超收敛分析[J]. 信阳师范学院学报(自然科学版), 2020, 33(2): 173-180. DOI: 10.3969/j.issn.1003-0972.2020.02.001
引用本文: 石东洋, 位一凡. Allen-Cahn方程的非协调元二重网格方法的超收敛分析[J]. 信阳师范学院学报(自然科学版), 2020, 33(2): 173-180. DOI: 10.3969/j.issn.1003-0972.2020.02.001
SHI Dongyang, WEI Yifan. Superconvergence Analysis of a Two-grid Method with Nonconforming Element for Allen-Cahn Equation[J]. Journal of Xinyang Normal University (Natural Science Edition), 2020, 33(2): 173-180. DOI: 10.3969/j.issn.1003-0972.2020.02.001
Citation: SHI Dongyang, WEI Yifan. Superconvergence Analysis of a Two-grid Method with Nonconforming Element for Allen-Cahn Equation[J]. Journal of Xinyang Normal University (Natural Science Edition), 2020, 33(2): 173-180. DOI: 10.3969/j.issn.1003-0972.2020.02.001

Allen-Cahn方程的非协调元二重网格方法的超收敛分析

Superconvergence Analysis of a Two-grid Method with Nonconforming Element for Allen-Cahn Equation

  • 摘要: 利用EQ1rot非协调有限元对Allen-Cahn方程建立一个关于时间有二阶精度的二重网格算法.借助于单元的特殊性质、导数转移技巧和插值后处理技术,在离散的H1模意义下得到了Oh2+H4+τ2)阶的超逼近和超收敛结果.给出了数值算例以验证理论的正确性与算法的高效性.这里hHτ分别表示细网格、粗网格的剖分尺度和时间步长.

     

    Abstract: A second order two-grid algorithm for Allen-Cahn equation is developed by using the nonconforming EQ1rot finite element. Based on the special properties of this element, the derivative transfer technique and the interpolated postprocessing approach, the superclose and superconvergence results of order O(h2+H4+τ2) in the broken H1-norm are deduced. A numerical example is given to verify the theoretical predictions and to show the efficiency of the proposed method. Here, h,H and τ represent the mesh size of fine grid, mesh size of coarse grid and time step size, respectively.

     

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