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On saturation effects in the Neumann boundary control of elliptic optimal control problems

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Abstract

A Neumann boundary control problem for a linear-quadratic elliptic optimal control problem in a polygonal domain is investigated. The main goal is to show an optimal approximation order for discretized problems after a postprocessing process. It turns out that two saturation processes occur: The regularity of the boundary data of the adjoint is limited if the largest angle of the polygon is at least 2π/3. Moreover, piecewise linear finite elements cannot guarantee the optimal order, if the largest angle of the polygon is greater than π/2. We will derive error estimates of order h α with α∈[1,2] depending on the largest angle and properties of the finite elements. Finally, numerical test illustrates the theoretical results.

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Authors and Affiliations

  1. Dpto. de Matemáticas, E.U.I.T.I. de Gijón, Universidad de Oviedo, Campus de Gijón, 33203, Gijón, Spain

    Mariano Mateos

  2. Fachbereich Mathematik, Universität Duisburg-Essen, Forsthausweg 2, 47057, Duisburg, Germany

    Arnd Rösch

Authors
  1. Mariano Mateos
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  2. Arnd Rösch
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Correspondence to Mariano Mateos.

Additional information

The first author was partially supported by the Spanish Ministry of Science and Innovation under project MTM2008-04206.

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Mateos, M., Rösch, A. On saturation effects in the Neumann boundary control of elliptic optimal control problems. Comput Optim Appl 49, 359–378 (2011). https://doi.org/10.1007/s10589-009-9299-5

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  • DOI: https://doi.org/10.1007/s10589-009-9299-5

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