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Volume 36, Issue 2
Meshfree Finite Volume Element Method for Constrained Optimal Control Problem Governed by Random Convection Diffusion Equations

Liang Ge, Wanfang Shen & Wenbin Liu

Commun. Math. Res., 36 (2020), pp. 229-246.

Published online: 2020-05

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  • 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.

  • Keywords

Optimal control problem, stochastic convection diffusion equations, meshfree method, radial basis functions, finite volume element.

  • AMS Subject Headings

49J20, 65N35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-36-229, author = {Liang and Ge and and 7677 and and Liang Ge and Wanfang and Shen and and 8190 and and Wanfang Shen and Wenbin and Liu and and 8191 and and Wenbin Liu}, 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} }
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.

Liang Ge, Wanfang Shen & Wenbin Liu. (2020). Meshfree Finite Volume Element Method for Constrained Optimal Control Problem Governed by Random Convection Diffusion Equations. Communications in Mathematical Research . 36 (2). 229-246. doi:10.4208/cmr.2020-0008
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