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.
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页码：2988 / 3011
页数：24
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