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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Affiliation: | 1.Dpto. de Matemáticas, E.U.I.T.I. de Gijón,Universidad de Oviedo,Gijón,Spain;2.Fachbereich Mathematik,Universit?t Duisburg-Essen,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 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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