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Extended finite element methods for optimal control problems governed by Poisson equation in non-convex domains

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Abstract

This paper analyzes two eXtended finite element methods (XFEMs) for linear quadratic optimal control problems governed by Poisson equation in non-convex domains. We follow the variational discretization concept to discretize the continuous problems, and apply an XFEM with a cut-off function and a classic XFEM with a fixed enrichment area to discretize the state and co-state equations. Optimal error estimates are derived for the state, co-state and control. Numerical results confirm our theoretical results.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11771312).

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  1. Chaochao Yang

    Present address: Current address: School of Science, Chongqing University of Technology, Chongqing, 400054, China

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  1. School of Mathematics, Sichuan University, Chengdu, 610064, China

    Tao Wang, Chaochao Yang & ** **e

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Wang, T., Yang, C. & **e, X. Extended finite element methods for optimal control problems governed by Poisson equation in non-convex domains. Sci. China Math. 64, 1917–1934 (2021). https://doi.org/10.1007/s11425-018-9487-4

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  • DOI: https://doi.org/10.1007/s11425-018-9487-4

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