Spectral mixed Galerkin method for state constrained optimal control problem governed by the first bi-harmonic equation

被引：26

作者：

Zhou, Jianwei ^{[1
]}

Yang, Danping ^{[1
]}

机构：

[1] E China Normal Univ, Dept Math, Shanghai 200062, Peoples R China

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2011年 / 88卷 / 14期

基金：

中国国家自然科学基金;

关键词：

optimal control; state constraint; bi-harmonic equation; mixed formulation; gradient projection algorithm; a priori error estimate; FINITE-ELEMENT; BIHARMONIC EQUATION; DIRECT SOLVERS; POLYNOMIALS; 2ND-ORDER;

D O I：

10.1080/00207160.2011.563845

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An optimal control problem governed by the first bi-harmonic equation with the integral constraint for the state and its spectral approximations based on a mixed formulation are investigated. The optimality conditions of the exact and the discrete optimal control systems are derived. The a priori error estimates of high order spectral accuracy are obtained. Furthermore, a simple and efficient iterative algorithm is proposed to solve mixed discrete system. Some numerical examples are performed to verify the theoretical results.

引用

页码：2988 / 3011

页数：24

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