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Numerical analysis of a control and state constrained elliptic control problem with piecewise constant control approximations. (English) Zbl 1157.65400

Kunisch, Karl (ed.) et al., Numerical mathematics and advanced applications. Proceedings of ENUMATH 2007, the 7th European conference on numerical mathematics and advanced applications, Graz, Austria, September 10–14, 2007. Berlin: Springer (ISBN 978-3-540-69776-3/hbk). 597-604 (2008).
Summary: 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.
For the entire collection see [Zbl 1145.65001].

MSC:

65K10 Numerical optimization and variational techniques
49J20 Existence theories for optimal control problems involving partial differential equations
49M15 Newton-type methods
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