Numerical Analysis of a Control and State Constrained Elliptic Control Problem with Piecewise Constant Control Approximations

K. Deckelnick () and M. Hinze ()
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K. Deckelnick: Otto-von-Guericke-Universität Magdeburg, Institut für Analysis und Numerik
M. Hinze: Universität Hamburg, Schwerpunkt Optimierung und Approximation

A chapter in Numerical Mathematics and Advanced Applications, 2008, pp 597-604 from Springer

Abstract: Abstract We consider an elliptic optimal control problem with control and pointwise state constraints. The cost functional is approximated by a sequence of functionals which are obtained by discretizing the state equation with the help of linear finite elements and enforcing the state constraints in the nodes of the triangulation. Controls are discretized piecewise constant on every simplex of the triangulation. Error bounds for control and state are obtained both in two and three space dimensions.

Keywords: State Constraint; Element Approximation; Unique Weak Solution; Interpolation Estimate; Piecewise Constant Control (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-69777-0_71

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DOI: 10.1007/978-3-540-69777-0_71

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