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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

DOI: 10.4208/cmr.2020-0008

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 = {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} }
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.

Ge , LiangShen , Wanfang and Liu , Wenbin. (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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