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Allen-Cahn方程的非协调元二重网格方法的超收敛分析

石东洋,  位一凡

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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
shu
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
shu

Allen-Cahn方程的非协调元二重网格方法的超收敛分析

doi: 10.3969/j.issn.1003-0972.2020.02.001

  • 郑州大学 数学与统计学院, 河南 郑州 450001

基金项目: 

国家自然科学基金项目（11671369）

详细信息
    作者简介:

    石东洋(1961-),男,河南鲁山人,河南省特聘教授,博士生导师,主要从事有限元方法及其应用研究.

  • 中图分类号: O242.21

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

  • School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China

  • 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O（h2+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h、H和τ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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出版历程
  • 收稿日期:  2019-08-06
  • 修回日期:  2019-11-06
  • 刊出日期:  2020-04-10

Allen-Cahn方程的非协调元二重网格方法的超收敛分析

doi: 10.3969/j.issn.1003-0972.2020.02.001
  • 郑州大学 数学与统计学院, 河南 郑州 450001
    • 基金项目:

    国家自然科学基金项目（11671369）

    作者简介:

    石东洋(1961-),男,河南鲁山人,河南省特聘教授,博士生导师,主要从事有限元方法及其应用研究.

  • 收稿日期: 2019-08-06
  • 修回日期: 2019-11-06
  • 刊出日期: 2020-04-10

  • 中图分类号: O242.21

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O（h2+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h、H和τ分别表示细网格、粗网格的剖分尺度和时间步长.

English Abstract

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
shu
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
shu

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