Convergence Analysis and Error Estimate for Distributed Optimal Control Problems Governed by Stokes Equations with Velocity-Constraint  

作　　者：Liang Ge Haifeng Niu Jianwei Zhou 

机构地区：[1]School of Mathematical Sciences,University of Jinan,Jinan 250022,Shandong,China [2]School of Mathematics and Information Science,Henan Polytechnic University,Jiaozuo 454000,Henan,China [3]School of Mathematics and Statistics,Linyi University,Linyi 276005,Shandong,China [4]Division of Applied and Computational Mathematics,Beijing Computational Science Research Center,Beijing 100193,China

出　　处：《Advances in Applied Mathematics and Mechanics》2022年第1期33-55,共23页应用数学与力学进展（英文）

基　　金：supported by NSFC grants(Nos.11926355,and 11701253);NSF of Henan Province(No.15A110024);NSF of Shandong Province(Nos.ZR2019YQ05,2019KJI003,and 2017GSF216001);China Postdoctoral Science Foundation(Nos.2017T100030,and 2017M610751)。

摘　　要：In this paper,spectral approximations for distributed optimal control problems governed by the Stokes equation are considered.And the constraint set on velocity is stated with L2-norm.Optimality conditions of the continuous and discretized systems are deduced with the Karush-Kuhn-Tucker conditions and a Lagrange multiplier depending on the constraint.To solve the equivalent systems with high accuracy,Galerkin spectral approximations are employed to discretize the constrained optimal control systems.Meanwhile,we adopt a parameter l in the pressure approximation space,which also guarantees the inf-sup condition,and study a priori error estimates for the velocity and pressure.Specially,an efficient algorithm based on the Uzawa algorithm is proposed and its convergence results are investigated with rigorous analyses.Numerical experiments are performed to confirm the theoretical results.

关 键 词：Optimal control spectral approximation Stokes equation convergence analysis 

分 类 号：O241.82[理学—计算数学]