TY - JOUR T1 - Meshfree Finite Volume Element Method for Constrained Optimal Control Problem Governed by Random Convection Diffusion Equations AU - Ge , Liang AU - Shen , Wanfang AU - Liu , Wenbin JO - Communications in Mathematical Research VL - 2 SP - 229 EP - 246 PY - 2020 DA - 2020/05 SN - 36 DO - http://doi.org/10.4208/cmr.2020-0008 UR - https://global-sci.org/intro/article_detail/cmr/16930.html KW - Optimal control problem, stochastic convection diffusion equations, meshfree method, radial basis functions, finite volume element. AB -

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.