no. 5
Optimal control/Numerical analysis
On a finite element method for measure-valued optimal control problems governed by the 1D generalized wave equation
[Sur une méthode d'éléments finis pour résoudre des problèmes de contrôle optimal régis par l'équation d'onde unidimensionnelle généralisée]

Présenté par : the Editorial Board

Vexler, Boris1 ; Zlotnik, Alexander2 ; Trautmann, Philip3
1 Zentrum Mathematik, Technische Universität München, Boltzmannstraße 3, 85748 Garching bei München, Germany
2 Department of Mathematics at Faculty of Economic Sciences, National Research University Higher School of Economics, Myasnitskaya 20, 101000 Moscow, Russia
3 Department of Mathematics and Scientific Computing, University of Graz, Heinrichstraße 36, 8010 Graz, Austria
Comptes Rendus. Mathématique, Tome 356 (2018) no. 5, pp. 523-531.

Cet article traite des problèmes de contrôle optimal régis par l'équation d'onde 1D avec coefficients variables, les espaces de contrôle étant, soit des fonctions mesurées Lw⁎2(I,M(Ω)), soit des mesures vectorielles M(Ω,L2(I)). On construit des discrétisations bilinéaires des éléments finis et on en analyse la stabilité et l'erreur.

The paper deals with the optimal control problems governed by the 1D wave equation with variable coefficients and the control spaces of either measure-valued functions Lw⁎2(I,M(Ω)) or vector measures M(Ω,L2(I)). Bilinear finite element discretizations are constructed and their stability and error analysis is accomplished.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2018.02.011
Vexler, Boris 1 ; Zlotnik, Alexander 2 ; Trautmann, Philip 3

1 Zentrum Mathematik, Technische Universität München, Boltzmannstraße 3, 85748 Garching bei München, Germany
2 Department of Mathematics at Faculty of Economic Sciences, National Research University Higher School of Economics, Myasnitskaya 20, 101000 Moscow, Russia
3 Department of Mathematics and Scientific Computing, University of Graz, Heinrichstraße 36, 8010 Graz, Austria 
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Vexler, Boris; Zlotnik, Alexander; Trautmann, Philip. On a finite element method for measure-valued optimal control problems governed by the 1D generalized wave equation. Comptes Rendus. Mathématique, Tome 356 (2018) no. 5, pp. 523-531. doi : 10.1016/j.crma.2018.02.011. http://www.numdam.org/articles/10.1016/j.crma.2018.02.011/

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