Abstract
We consider a simple parabolic free boundary problem and formulate this problem as an optimal control problem. In order to compute the solution of the control problem we apply the gradient method. Furthermore we consider the discrete control problem and in the case of an implicit free boundary problem we show convergence of the solution of the discrete problem to the solution of the continuous problem. Some numerical examples illustrate the results.
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Literatur
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Baumeister, J. (1978). Ein Iterationsverfahren zur Lösung eines Parabolischen Freien Randwertproblems. In: Albrecht, J., Collatz, L., Hämmerlin, G. (eds) Numerische Behandlung von Differentialgleichungen mit besonderer Berücksichtigung freier Randwertaufgaben. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 39. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5566-2_2
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DOI: https://doi.org/10.1007/978-3-0348-5566-2_2
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-0986-2
Online ISBN: 978-3-0348-5566-2
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