A Posteriori Error Estimates of Mixed Methods for Quadratic Optimal Control Problems Governed by Parabolic Equations

被引：3

作者：

Hou, Tianliang ^{[2
]}

Chen, Yanping ^{[1
]}

Huang, Yunqing ^{[2
]}

机构：

[1] S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China

[2] Xiangtan Univ, Dept Math, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Hunan, Peoples R China

来源：

NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS | 2011年 / 4卷 / 04期

基金：

美国国家科学基金会;

关键词：

A posteriori error estimates; quadratic optimal control problems; parabolic equations; mixed finite element methods; FINITE-ELEMENT APPROXIMATION; BOUNDARY CONTROL-PROBLEMS;

D O I：

10.4208/nmtma.2011.m1017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we discuss the a posteriori error estimates of the mixed finite element method for quadratic optimal control problems governed by linear parabolic equations. The state and the co-state are discretized by the high order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. We derive a posteriori error estimates for both the state and the control approximation. Such estimates, which are apparently not available in the literature, are an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.

引用

页码：439 / 458

页数：20

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