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

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

doi: 10.3969/j.issn.1003-0972.2020.02.001
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

  • 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.
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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
    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.

  • 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.

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
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
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