@Article{CMR-36-229, author = {Ge , LiangShen , Wanfang and Liu , Wenbin}, title = {Meshfree Finite Volume Element Method for Constrained Optimal Control Problem Governed by Random Convection Diffusion Equations}, journal = {Communications in Mathematical Research }, year = {2020}, volume = {36}, number = {2}, pages = {229--246}, abstract = {

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.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2020-0008}, url = {http://global-sci.org/intro/article_detail/cmr/16930.html} }