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Superconvergence for Neumann boundary control problems governed by semilinear elliptic equations

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  • K. Krumbiegel
  • J. Pfefferer

Abstract

This paper is concerned with the discretization error analysis of semilinear Neumann boundary control problems in polygonal domains with pointwise inequality constraints on the control. The approximations of the control are piecewise constant functions. The state and adjoint state are discretized by piecewise linear finite elements. In a postprocessing step approximations of locally optimal controls of the continuous optimal control problem are constructed by the projection of the respective discrete adjoint state. Although the quality of the approximations is in general affected by corner singularities a convergence order of $$h^2|\ln h|^{3/2}$$ h 2 | ln h | 3 / 2 is proven for domains with interior angles smaller than $$2\pi /3$$ 2 π / 3 using quasi-uniform meshes. For larger interior angles mesh grading techniques are used to get the same order of convergence. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • K. Krumbiegel & J. Pfefferer, 2015. "Superconvergence for Neumann boundary control problems governed by semilinear elliptic equations," Computational Optimization and Applications, Springer, vol. 61(2), pages 373-408, June.
    • Handle: RePEc:spr:coopap:v:61:y:2015:i:2:p:373-408
    DOI: 10.1007/s10589-014-9718-0
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    References listed on IDEAS

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    1. Thomas Apel & Johannes Pfefferer & Arnd Rösch, 2012. "Finite element error estimates for Neumann boundary control problems on graded meshes," Computational Optimization and Applications, Springer, vol. 52(1), pages 3-28, May.
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    Cited by:

    1. Max Winkler, 2020. "Error estimates for the finite element approximation of bilinear boundary control problems," Computational Optimization and Applications, Springer, vol. 76(1), pages 155-199, May.

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