Article Dans Une Revue Mathematical Control and Related Fields Année : 2019

APPROXIMATION OF CONTROLS FOR LINEAR WAVE EQUATIONS: A FIRST ORDER MIXED FORMULATION

Résumé

This paper deals with the numerical approximation of null controls for the wave equation posed in a bounded domain of R n. The goal is to compute approximations of controls that drive the solution from a prescribed initial state to zero at a large enough controllability time. In [Cindea & Münch, A mixed formulation for the direct approximation of the control of minimal L 2-norm for linear type wave equations], we have introduced a space-time variational approach ensuring strong convergent approximations with respect to the discretization parameter. The method, which relies on generalized ob-servability inequality, requires H 2-finite element approximation both in time and space. Following a similar approach, we present and analyze a variational method still leading to strong convergent results but using simpler H 1-approximation. The main point is to preliminary restate the second order wave equation into a first order system and then prove an appropriate observability inequality.

Fichier principal
Vignette du fichier
Montaner_Munch_FirstOrder2018.pdf (1.71 Mo) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence
Loading...

Dates et versions

hal-01792949 , version 1 (16-05-2018)

Licence

Identifiants

Citer

Santiago Montaner, Arnaud Münch. APPROXIMATION OF CONTROLS FOR LINEAR WAVE EQUATIONS: A FIRST ORDER MIXED FORMULATION. Mathematical Control and Related Fields, 2019, 9 (4), pp.729-758. ⟨10.3934/mcrf.2019030⟩. ⟨hal-01792949⟩
353 Consultations
1009 Téléchargements

Altmetric

Partager

  • More