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平面弹性问题自适应有限元方法的收敛性分析

刘春梅 钟柳强 舒适 肖映雄

刘春梅, 钟柳强, 舒适, 肖映雄. 平面弹性问题自适应有限元方法的收敛性分析[J]. 应用数学和力学, 2014, 35(9): 969-978. doi: 10.3879/j.issn.1000-0887.2014.09.003
引用本文: 刘春梅, 钟柳强, 舒适, 肖映雄. 平面弹性问题自适应有限元方法的收敛性分析[J]. 应用数学和力学, 2014, 35(9): 969-978. doi: 10.3879/j.issn.1000-0887.2014.09.003
LIU Chun-mei, ZHONG Liu-qiang, SHU Shi, XIAO Ying-xiong. Convergence of an Adaptive Finite Element Method for 2D Elasticity Problems[J]. Applied Mathematics and Mechanics, 2014, 35(9): 969-978. doi: 10.3879/j.issn.1000-0887.2014.09.003
Citation: LIU Chun-mei, ZHONG Liu-qiang, SHU Shi, XIAO Ying-xiong. Convergence of an Adaptive Finite Element Method for 2D Elasticity Problems[J]. Applied Mathematics and Mechanics, 2014, 35(9): 969-978. doi: 10.3879/j.issn.1000-0887.2014.09.003

平面弹性问题自适应有限元方法的收敛性分析

doi: 10.3879/j.issn.1000-0887.2014.09.003
基金项目: 湖南省自然科学基金(14JJ3135); 国家自然科学基金(11201159);全国博士学位论文作者专项资金(201212);广东省高等学校优秀青年教师培养计划(Yq2013054); 广州市珠江科技新星项目(2013J2200063)
详细信息
    作者简介:

    刘春梅(1981—), 女, 山西人, 讲师, 博士(E-mail: liuchunmei0629@163.com);舒适(1962—), 男,湖南人, 教授, 博士, 博士生导师(通讯作者. E-mail: shushi@xtu.edu.cn).

  • 中图分类号: O241.8;O242

Convergence of an Adaptive Finite Element Method for 2D Elasticity Problems

Funds: The National Natural Science Foundation of China(11201159)
  • 摘要: 针对平面弹性问题,首先采用基于最新顶点二分法的网格加密方法,给出一种不需要标记振荡项和加密单元、不需要满足“内节点”性质的自适应有限元方法.其次,通过对各层网格上解函数和误差指示子的分析,利用相邻网格层上解函数的正交性、解函数和真解函数的能量误差的上界估计、相邻网格层上误差指示子的近似压缩性等结果,从理论上严格证明了该自适应有限元方法是收敛的.最后数值实验验证了该自适应有限元方法是收敛的和鲁棒的.
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出版历程
  • 收稿日期:  2014-01-20
  • 刊出日期:  2014-09-15

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