Computational Optimization and Applications

, Volume 61, Issue 2, pp 373–408 | Cite as

Superconvergence for Neumann boundary control problems governed by semilinear elliptic equations

Article

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 \(h^2|\ln h|^{3/2}\) is proven for domains with interior angles smaller than \(2\pi /3\) using quasi-uniform meshes. For larger interior angles mesh grading techniques are used to get the same order of convergence.

Keywords

Semilinear elliptic Neumann boundary control problem Finite element error estimates  Graded meshes Postprocessing  Superconvergence 

Mathematics Subject Classification

65N30 49K20 49M25 65N15 65N50 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Institute for Applied Mathematics and Stochastics, Nonlinear Optimization and Inverse ProblemsBerlinGermany
  2. 2.Universität der Bundeswehr MünchenNeubibergGermany

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