Superconvergence of Rectangular Mixed Finite Element Methods for Constrained Optimal Control Problem

被引：13

作者：

Chen, Yanping ^{[1
]}

Dai, Li ^{[2
]}

Lu, Zuliang ^{[3
]}

机构：

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

[2] Xiguan Foreign Language Sch, Math Teaching & Res Grp, Guangzhou, Guangdong, Peoples R China

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

来源：

ADVANCES IN APPLIED MATHEMATICS AND MECHANICS | 2010年 / 2卷 / 01期

基金：

美国国家科学基金会;

关键词：

Constrained optimal control problem; linear elliptic equation; mixed finite element methods; rectangular partition; superconvergence properties; QUADRATIC OPTIMAL-CONTROL; APPROXIMATION; EQUATIONS;

D O I：

10.4208/aamm.09-m0931

中图分类号：

O29 [应用数学];

学科分类号：

070104 [应用数学];

摘要：

We investigate the superconvergence properties of the constrained quadratic elliptic optimal control problem which is solved by using rectangular mixed finite element methods. We use the lowest order Raviart-Thomas mixed finite element spaces to approximate the state and co-state variables and use piece-wise constant functions to approximate the control variable. We obtain the superconvergence of O(h(1+s)) (0<s <= 1) for the control variable. Finally, we present two numerical examples to confirm our superconvergence results.

引用

页码：56 / 75

页数：20

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Adams R., 1985, Sobolev Spaces

[2]

[Anonymous], 1977, MATH ASPECTS FINITE

[3]

Error estimates for the numerical approximation of a semilinear elliptic control problem [J].