Meshfree Finite Volume Element Method for Constrained Optimal Control Problem Governed by Random Convection Diffusion Equations  

作　　者：Liang Ge Wanfang Shen Wenbin Liu 

机构地区：[1]School of Mathematical Sciences,University of Jinan,Jinan,Shandong 250022,China [2]School of Mathematic and Quantitative Economics,Shandong Key Laboratory of Blockchain Finance,Shandong University of Finance and Economics,Jinan,Shandong 250014,China [3]Beijing Normal University,Beijing 100875 [4]Beijing Normal University–Hong Kong Baptist University United International College,Zhuhai,Guangdong,519087,China.

出　　处：《Communications in Mathematical Research》2020年第2期229-246,共18页数学研究通讯（英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.11701253,11971259,11801216);Natural Science Foundation of Shandong Province(No.ZR2017BA010)。

摘　　要：In this paper,we investigate a stochastic meshfree finite volume element method for an optimal control problem governed by the convection diffusion equations with random coefficients.There are two contributions of this paper.Firstly,we establish a scheme to approximate the optimality system by using the finite volume element method in the physical space and the meshfree method in the probability space,which is competitive for high-dimensional random inputs.Secondly,the a priori error estimates are derived for the state,the co-state and the control variables.Some numerical tests are carried out to confirm the theoretical results and demonstrate the efficiency of the proposed method.

关 键 词：Optimal control problem stochastic convection diffusion equations meshfree method radial basis functions finite volume element 

分 类 号：O241.82[理学—计算数学]