Abstract
An optimal control problem for a 2-d elliptic equation and with pointwise control constraints is investigated. The domain is assumed to be polygonal but non-convex. The corner singularities are treated by a priori mesh grading. A second order approximation of the optimal control is constructed by a projection of the discrete adjoint state. Here we summarize the results from [1] and add further numerical tests.
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References
Apel, T., Rösch, A., Winkler, G.: Optimal control in nonconvex domains. RICAM Report, 17 (2005-17). http://www.ricam.oeaw.ac.at/publications/reports/.
Hinze, M.: A variational discretization concept in control constrained optimization: The linear-quadratic case. Computational Optimization and Applications, 30 45–63 (2005)
Meyer, C., Rösch, A.: Superconvergence properties of optimal control problems. SIAM J. Control and Optimization, 43 970–985 (2004)
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Apel, T., Rösch, A., Winkler, G. (2006). Discretization Error Estimates for an Optimal Control Problem in a Nonconvex Domain. In: de Castro, A.B., Gómez, D., Quintela, P., Salgado, P. (eds) Numerical Mathematics and Advanced Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34288-5_23
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DOI: https://doi.org/10.1007/978-3-540-34288-5_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34287-8
Online ISBN: 978-3-540-34288-5
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