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Residual-type a posteriori error analysis of HDG methods for Neumann boundary control problems

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Abstract

We study a posteriori error analysis of linear-quadratic boundary control problems under bilateral box constraints on the control which acts through a Neumann-type boundary condition. We adopt the hybridizable discontinuous Galerkin method as the discretization technique, and the flux variables, the scalar variables, and the boundary trace variables are all approximated by polynomials of degree k. As for the control variable, it is discretized by the variational discretization concept. Then, an efficient and reliable a posteriori error estimator is introduced, and we prove that the error estimator provides an upper bound and a lower bound for the errors. Finally, numerical results are presented to illustrate the performance of the obtained a posteriori error estimator.

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Funding

The work of Haitao Leng was supported by the Cultivation Project of SCNU (Grant No. 19KJ08) and the NSF of China (Grant No. 12001209). The work of Yanping Chen was supported by the State Key Program of NSF of China (11931003) and the NSF of China (41974133, 11671157).

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Authors and Affiliations

  1. School of Mathematical Sciences, South China Normal University, Guangzhou, Guangdong, 510631, China

    Haitao Leng & Yanping Chen

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  1. Haitao Leng
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  2. Yanping Chen
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Correspondence to Yanping Chen.

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Communicated by: Peter Benner

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Leng, H., Chen, Y. Residual-type a posteriori error analysis of HDG methods for Neumann boundary control problems. Adv Comput Math 47, 30 (2021). https://doi.org/10.1007/s10444-021-09864-9

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  • DOI: https://doi.org/10.1007/s10444-021-09864-9

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