Abstract
AbstractA 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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