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

Arnaud Munch (1) , Santiago Montaner (2)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 LMBP - Laboratoire de Mathématiques Blaise Pascal

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.

Domaines: Optimisation et contrôle [math.OC]

Arnaud Munch, Santiago Montaner. APPROXIMATION OF CONTROLS FOR LINEAR WAVE EQUATIONS: A FIRST ORDER MIXED FORMULATION. 2018. ⟨hal-01792949⟩