On saturation effects in the Neumann boundary control of elliptic optimal control problems |
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| Authors: | Mariano Mateos Arnd Rösch |
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| Institution: | 1. Dpto de Matemáticas, E.P.S.I. de Gijón, Universidad de Oviedo, Campus de Viesques, 33203 Gijón, Spain;2. Universität Duisburg-Essen, Fachbereich Mathematik, Forsthausweg 2, D-47057 Duisburg, Germany |
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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 state 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 hσ with σ ∈ 3/2, 2] depending on the largest angle and properties of the finite elements. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) |
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