Nonconforming finite element scheme for constrained optimal control problems governed by Maxwell’s equations

Yuhui Xiao; Jianping Zhao; Yanren Hou

doi:10.1117/12.2686145

28 July 2023 Nonconforming finite element scheme for constrained optimal control problems governed by Maxwell’s equations

Yuhui Xiao, Jianping Zhao, Yanren Hou

Author Affiliations +

Proceedings Volume 12756, 3rd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2023); 127560W (2023) https://doi.org/10.1117/12.2686145
Event: 2023 3rd International Conference on Applied Mathematics, Modelling and Intelligent Computing (CAMMIC 2023), 2023, Tangshan, China

Abstract

In this paper, we present and analyze the Nonconforming finite element method (NFEM) for constrained optimal control problems governed by Maxwell’s equations. Firstly, based on Maxwell’s equations, we propose the elliptic optimal control problem in H(curl) space, establish an optimal control system and give the regularity property of the optimal control model. Then, the state and co-state variables are discretized by NFEM, the control variable is approximated by piecewise constants element. The L² -norm for control and the semi-norm for state and co-state are derived. At last, numering results illustrating the theoretical findings.

Citation Download Citation

Yuhui Xiao, Jianping Zhao, and Yanren Hou "Nonconforming finite element scheme for constrained optimal control problems governed by Maxwell’s equations", Proc. SPIE 12756, 3rd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2023), 127560W (28 July 2023); https://doi.org/10.1117/12.2686145

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