对流扩散方程最优控制问题的重心插值配点格式  

Barycentric Interpolation Collocation Format for Optimal Control Problem of Convection-Diffusion Equation

作　　者：黄蓉 姚梦丽 翁智峰 HUANG Rong;YAO Mengli;WENG Zhifeng(School of Mathematical Sciences,Huaqiao University,Quanzhou 362021,China)

机构地区：[1]华侨大学数学科学学院,福建泉州362021

出　　处：《华侨大学学报（自然科学版）》2023年第3期407-416,共10页Journal of Huaqiao University(Natural Science)

基　　金：国家自然科学基金资助项目(11701197);中央高校基本科研业务费专项资金资助项目(ZQN-702)。

摘　　要：为了讨论对流扩散方程最优控制问题的重心插值配点格式,首先,借助Lagrange乘子法,推导出由状态方程、伴随方程、最优性方程构成的最优性条件.其次,在空间x,y方向均运用重心插值配点格式离散方程组,并给出该配点格式的相容性分析.最后,数值实验验证格式的有效性,与经典有限差分格式比较,重心插值配点格式用较少的节点数就能具有很高的精度.The barycentric interpolation collocation format for optimal control problem of convection-diffusion equationis considered.Firstly,the optimality conditions which are composed of the state equation,adjoint equation and optimality equation are derived by Lagrange multiplier method.Secondly,the barycentric interpolation collocation format is used to discretize equations in the directions of x and y in space,and the consistent error analysis of the collocation format is also given.Finally,numerical experiments verify the effectiveness of the collocation format.Compared with the classical finite difference format,the barycentric interpolation collocation format has higher accuracy with fewer node numbers.

关 键 词：重心插值配点格式 对流扩散方程 最优控制问题 误差分析 LAGRANGE乘子法 

分 类 号：O241.82[理学—计算数学]