Meshfree Finite Volume Element Method for Constrained Optimal Control Problem Governed by Random Convection Diffusion Equations (Communications in Mathematical Research, 2022)
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 thispaper. Firstly, we establish a scheme to approximate the optimality system byusing the finite volume element method in the physical space and the meshfreemethod in the probability space, which is competitive for high-dimensionalrandom 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 toconfirm the theoretical results and demonstrate the efficiency of the proposedmethod.
Keywords: Optimal control problem; stochastic convection diffusion equations; meshfree method; radial basis functions; finite volume element.