A FULL DISCRETE STABILIZED METHOD FOR THE OPTIMAL CONTROL OF THE UNSTEADY NAVIER-STOKES EQUATIONS  

作　　者：Yanmei Qin Gang Chen Minfu Feng 

机构地区：[1]Key Laboratory of Numerical Simulation of Sichuan Province, Neijiang Normal University, Neijiang 641002, China [2]School of Mathematics Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China [3]School of Mathematics, Sichuan University, Chengdu 610064, China

出　　处：《Journal of Computational Mathematics》2018年第5期718-738,共21页计算数学（英文）

基　　金：This work is supported by the Natural Science Foundation of China （No. 11271273） and the Scientific Research Foundation of the Education Department of Sichuan Province of China （No.16ZB0300）. The authors would like to thank the associate editor and anonymous referees comments to improve the quality of the manuscript.

摘　　要：In this paper, a full discrete local projection stabilized （LPS） method is proposed to solve the optimal control problems of the unsteady Navier-Stokes equations with equal order elements. Convective effects and pressure are both stabilized by using the LPS method. A priori error estimates uniformly with respect to the Reynolds number are obtained, providing the true solutions are sufficient smooth. Numerical experiments are implemented to illustrate and confirm our theoretical analysis.In this paper, a full discrete local projection stabilized （LPS） method is proposed to solve the optimal control problems of the unsteady Navier-Stokes equations with equal order elements. Convective effects and pressure are both stabilized by using the LPS method. A priori error estimates uniformly with respect to the Reynolds number are obtained, providing the true solutions are sufficient smooth. Numerical experiments are implemented to illustrate and confirm our theoretical analysis.

关 键 词：Optimal control Unsteady Navier-Stokes equations High Reynolds number Full discrete Local projection stabilization. 

分 类 号：O231[理学—运筹学与控制论] TQ028.8[理学—数学]