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一类椭圆最优控制问题的最大模估计
  • ISSN号：1000-5900
  • 期刊名称：《湘潭大学自然科学学报》
  • 时间：0
  • 分类：O175.25[理学—数学;理学—基础数学]
  • 作者机构：[1]华南师范大学数学科学学院,广东广州510631
  • 相关基金：国家自然科学基金项目（10971074）; 天元基金项目（11026092）
作者： 邢小青[1], 陈艳萍[1]
关键词： 最大模估计, 混合有限元, 最优控制, L^∞-error estimates, mixed finite element, optimal control
中文摘要：

采用混合有限元方法研究一类椭圆最优控制问题的最大模估计.对状态变量和对偶状态变量,采用最低阶的R-T混合有限元空间来逼近;对控制变量采用分片常数函数来逼近.通过引入投影算子,找到了对偶状态变量和控制变量之间的关系,进而得到了关于状态变量及控制变量的最优阶误差估计.最后给出了相应的数值算例.

英文摘要：

In this paper,we investigate the L∞-error estimates for the solutions of elliptic optimal control problem by mixed finite element methods.The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions.By introducing the projection,we find the relation between the co-state variable and the control variable.We derive L∞-error estimates of optimal order both for the state variables and the control variable.At last,a numerical test is presented.

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最优控制问题自适应混合有限元方法
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期刊信息
  • 《湘潭大学自然科学学报》
  • 北大核心期刊（2011版）
  • 主管单位:湖南省教育厅
  • 主办单位:湘潭大学
  • 主编：黄云清
  • 地址：湖南湘潭市
  • 邮编：411105
  • 邮箱：jxtus@xtu.edu.cn
  • 电话：0731-58292143
  • 国际标准刊号：ISSN：1000-5900
  • 国内统一刊号：ISSN：43-1066/N
  • 邮发代号:42-33
  • 获奖情况:
  • 全国优秀科技期刊,湖南省一级期刊
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国化学文摘（网络版）,美国数学评论（网络版）,德国数学文摘,荷兰文摘与引文数据库,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）
  • 被引量:4425