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 - <p style="text-align: justify;">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.</p>