.png){kind=icon}
返回
Error estimates for Neumann boundary control problems with energy regularization
.png){kind=icon}
PRE
AI
DOI：10.1515/jnma-2015-0072.png)
.png){kind=icon}
原文求助.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
A Neumann boundary control problem for a second order elliptic state equation is considered. The problem is regularized by an energy term which is equivalent to the H-1/2 (Gamma)-norm of the control. Both the unconstrained and the control constrained cases are investigated. The regularity of the state, control, and costate variables is studied with particular focus on the singularities due to the corners of the two-dimensional domain. The state and co-state are approximated by piecewise linear finite elements. For the approximation of the control variable we use carefully designed spaces of piecewise linear or piecewise constant functions, such that an inf-sup condition is satisfied. Error estimates for the approximate solution are proved for all three variables and we show a relation between convergence rate and the opening angles at corners of the domain. As the control grows in general unboundedly near the concave corners for unconstrained problems, it becomes active and hence regular when control constraints are present. We show that in this case the convergence rates are higher than in the unbounded case. Numerical tests suggest that the estimates derived are optimal in the unconstrained case but too pessimistic in the control constrained case.
Keyword:
optimal control
corner singularities
finite element method
error estimates
weighted Sobolev spaces
AI总结
对已上传原文的论文进行重点信息的提取，主要内容包括：简要概述、研究摘要、背景介绍、关键亮点、图文解析、展望与总结。
期刊
IF:
4
论文数:
308
被引数:
659
机构
引用论文
.png){kind=icon}
分享收藏Increasing the Automation Degree in Wiring Harness Assembly by Extending the Standard Crimping Machines by Developed Assembly Concept通过扩展标准压接机并采用开发的装配概念来提高线束组装的自动化程度
PREAI
分享收藏
没有更多内容
没有更多内容