A Priori Error Analysis for NCVEM Discretization of Elliptic Optimal Control Problem  

作　　者：Shiying Wang Shuo Liu Shiying Wang;Shuo Liu(School of Mathematics and Statistics, Shandong Normal University, Jinan, China)

机构地区：[1]School of Mathematics and Statistics, Shandong Normal University, Jinan, China

出　　处：《Engineering（科研）》2024年第4期83-101,共19页工程（英文）（1947-3931）

摘　　要：In this paper, we propose the nonconforming virtual element method (NCVEM) discretization for the pointwise control constraint optimal control problem governed by elliptic equations. Based on the NCVEM approximation of state equation and the variational discretization of control variables, we construct a virtual element discrete scheme. For the state, adjoint state and control variable, we obtain the corresponding prior estimate in H¹ and L² norms. Finally, some numerical experiments are carried out to support the theoretical results.In this paper, we propose the nonconforming virtual element method (NCVEM) discretization for the pointwise control constraint optimal control problem governed by elliptic equations. Based on the NCVEM approximation of state equation and the variational discretization of control variables, we construct a virtual element discrete scheme. For the state, adjoint state and control variable, we obtain the corresponding prior estimate in H¹ and L² norms. Finally, some numerical experiments are carried out to support the theoretical results.

关 键 词：Nonconforming Virtual Element Method Optimal Control Problem a Priori Error Estimate 

分 类 号：O17[理学—数学]