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A Multiscale Finite Element Method for an Elliptic Distributed Optimal Control Problem with Rough Coefficients and Control Constraints

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Abstract

We construct and analyze a multiscale finite element method for an elliptic distributed optimal control problem with pointwise control constraints, where the state equation has rough coefficients. We show that the performance of the multiscale finite element method is similar to the performance of standard finite element methods for smooth problems and present corroborating numerical results.

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Data Availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

Portions of this research were conducted with high performance computing resources provided by Louisiana State University (http://www.hpc.lsu.edu).

Funding

This work was supported in part by the National Science Foundation under Grant No. DMS-19-13035 and Grant No. DMS-22-08404.

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Authors and Affiliations

  1. Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, LA, 70803, USA

    Susanne C. Brenner & Li-yeng Sung

  2. Institute of Mathematics, Universtät Augsburg, 86159, Augsburg, Germany

    José C. Garay

Authors
  1. Susanne C. Brenner
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  2. José C. Garay
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  3. Li-yeng Sung
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Correspondence to Susanne C. Brenner.

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This work was supported in part by the National Science Foundation under Grant No. DMS-19-13035 and Grant No. DMS-22-08404.

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Brenner, S.C., Garay, J.C. & Sung, Ly. A Multiscale Finite Element Method for an Elliptic Distributed Optimal Control Problem with Rough Coefficients and Control Constraints. J Sci Comput 100, 47 (2024). https://doi.org/10.1007/s10915-024-02590-6

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  • DOI: https://doi.org/10.1007/s10915-024-02590-6

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