Superconvergence for Optimal Control Problems Governed by Semi-linear Elliptic Equations

被引：61
|
作者：
Chen, Yanping [1 ]
Dai, Yongquan [2 ]
机构：
[1] S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China
[2] Xiangtan Univ, Hunan Key Lab Computat & Simulat Sci & Engn, Dept Math, Xiangtan 411105, Peoples R China
来源：
JOURNAL OF SCIENTIFIC COMPUTING | 2009年 / 39卷 / 02期
基金：
美国国家科学基金会;
关键词：
Finite element approximation; Superconvergence; Semi-linear elliptic equation; Optimal control problem; Interpolate operator; MIXED FINITE-ELEMENT; OPTIMIZATION PROBLEMS; APPROXIMATION; 2ND-ORDER;
D O I：
10.1007/s10915-008-9258-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we will investigate the superconvergence of the finite element approximation for quadratic optimal control problem governed by semi-linear elliptic equations. The state and co-state variables are approximated by the piecewise linear functions and the control variable is approximated by the piecewise constant functions. We derive the superconvergence properties for both the control variable and the state variables. Finally, some numerical examples are given to demonstrate the theoretical results.
引用
收藏
页码：206 / 221
页数：16
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