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二维瞬态热传导问题的无单元Galerkin法分析

王红 李小林

王红, 李小林. 二维瞬态热传导问题的无单元Galerkin法分析[J]. 应用数学和力学, 2021, 42(5): 460-469. doi: 10.21656/1000-0887.410111
引用本文: 王红, 李小林. 二维瞬态热传导问题的无单元Galerkin法分析[J]. 应用数学和力学, 2021, 42(5): 460-469. doi: 10.21656/1000-0887.410111
WANG Hong, LI Xiaolin. Analysis of 2D Transient Heat Conduction Problems With the Element-Free Galerkin Method[J]. Applied Mathematics and Mechanics, 2021, 42(5): 460-469. doi: 10.21656/1000-0887.410111
Citation: WANG Hong, LI Xiaolin. Analysis of 2D Transient Heat Conduction Problems With the Element-Free Galerkin Method[J]. Applied Mathematics and Mechanics, 2021, 42(5): 460-469. doi: 10.21656/1000-0887.410111

二维瞬态热传导问题的无单元Galerkin法分析

doi: 10.21656/1000-0887.410111
基金项目: 国家自然科学基金(面上项目)(11971085);重庆市高校创新研究群体(CXQT19018);重庆市教委科学技术研究项目(重大项目)(KJZDM201800501)
详细信息
    作者简介:

    王红(1994—),女,硕士(E-mail: 1072835817@qq.com);李小林(1983—),男,教授(通讯作者. E-mail: lxlmath@163.com).

  • 中图分类号: O241.82

Analysis of 2D Transient Heat Conduction Problems With the Element-Free Galerkin Method

Funds: The National Natural Science Foundation of China(11971085)
  • 摘要: 采用无单元Galerkin(element-free Galerkin,EFG)法求解具有混合边界条件的二维瞬态热传导问题.首先采用二阶向后微分公式离散热传导方程的时间变量,将该问题转化为与时间无关的混合边值问题;然后采用罚函数法处理Dirichlet边界条件,建立了二维瞬态热传导问题的无单元Galerkin法;最后基于移动最小二乘近似的误差结果,详细推导了无单元Galerkin法求解二维瞬态热传导问题的误差估计公式.给出的数值算例表明计算结果与解析解或已有数值解吻合较好,该方法具有较高的计算精度和较好的收敛性.
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出版历程
  • 收稿日期:  2020-04-20
  • 修回日期:  2020-07-07
  • 刊出日期:  2021-05-01

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