| 一类抛物最优控制问题的有限元误差估计 |
| |
| 引用本文： | 王世杰,常延贞.一类抛物最优控制问题的有限元误差估计[J].北京化工大学学报(自然科学版),2018,45(6):106-110. |
| |
| 作者姓名： | 王世杰 常延贞 |
| |
| 作者单位： | 北京化工大学理学院,北京,100029;北京化工大学理学院,北京,100029 |
| |
| 摘 要： | 对一类抛物最优控制问题给出了有限元逼近格式，其中控制约束集为积分受限的形式K={u（t）∈L2（Ω）：a ≤ ∫Ω u（t）≤ b}。对问题的状态变量和伴随状态变量用线性连续函数离散，而控制变量使用分片常数近似；最后得到控制和状态变量逼近的先验误差估计O（h2+k）。
|
| 关 键 词： | 有限元逼近 积分受限最优控制 误差估计 抛物型方程 |
| 收稿时间： | 2017-11-24 |
Error estimates of the finite element method for a class of parabolic optimal control problems |
| |
| WANG ShiJie,CHANG YanZhen.Error estimates of the finite element method for a class of parabolic optimal control problems[J].Journal of Beijing University of Chemical Technology,2018,45(6):106-110. |
| |
| Authors: | WANG ShiJie CHANG YanZhen |
| |
| Institution: | Faculty of Science, Beijing University of Chemical Technology, Beijing 100029, China |
| |
| Abstract: | In this paper, we study a finite element approximation scheme for a class of parabolic optimal control problems. The control constraint is given in an integral sense:K={u(t)∈L2(Ω):a ≤ ∫Ω u(t) ≤ b}, where the state and co-state variables are discretized by piecewise linear continuous functions and the control variable is approximated by piecewise constant functions. Some error estimates are derived for both control and state approximations. It is proven that these approximations have convergence order O(h2+k). |
| |
| Keywords: | finite element approximation integral constrained optimal control error estimates parabolic equation |
| 本文献已被 万方数据 等数据库收录！ |
| 点击此处可从《北京化工大学学报(自然科学版)》浏览原始摘要信息 |
| 点击此处可从《北京化工大学学报(自然科学版)》下载免费的PDF全文 |
