控制-状态受限椭圆最优控制问题的新误差估计  

A New Error Estimates for Elliptic Optimal Control Problems with Control and State Constraints

作　　者：陈艳萍[1] 黄封林[1] 

机构地区：[1]华南师范大学数学科学学院,广州510631

出　　处：《华南师范大学学报（自然科学版）》2016年第5期86-91,共6页Journal of South China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(91430104;11271145)

摘　　要：构建了控制-状态积分受限椭圆最优控制问题的谱方法计算格式,推导了最优性条件,并利用收敛性结果和分类讨论的方法对拉格朗日乘子的逼近误差进行估计,进而得出了后验误差估计结果.文中为偏微分方程最优控制问题提供了具有高精度的求解方法,并为发展最优控制问题的hp自适应谱元方法计算奠定了基础.Galerkin spectral method is used to approximate elliptic optimal control problems with integral control and state constraints in this paper. The optimality conditions for the control problems are derived; the estimation for Lagrange multiplier is investigated by the convergence results and classification discussion; then a posteriori error estimates are presented. This work provides efficient numerical method with high-precision and lays the foundation for developing hp-adaptive spectral element method for optimal control problems of PDEs.

关 键 词：最优控制 椭圆方程 谱方法 误差估计 

分 类 号：O241.1[理学—计算数学]