Meshfree Finite Volume Element Method for Constrained Optimal Control Problem Governed by Random Convection Diffusion Equations
Year: 2020
Author: Liang Ge, Wanfang Shen, Wenbin Liu
Communications in Mathematical Research , Vol. 36 (2020), Iss. 2 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2020-0008
Communications in Mathematical Research , Vol. 36 (2020), Iss. 2 : pp. 229–246
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Optimal control problem stochastic convection diffusion equations meshfree method radial basis functions finite volume element.
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