Cindea, NicolaeFernández Cara, EnriqueMünch, Arnaud2016-07-042016-07-042013Cindea, N., Fernández Cara, E. y Münch, A. (2013). Numerical controllability of the wave equation through primal methods and Carleman estimates. ESAIM: Control, Optimisation and Calculus of Variations, 19, 1076-1108.1292-81191262-3377http://hdl.handle.net/11441/43112This paper deals with the numerical computation of boundary null controls for the 1D wave equation with a potential. 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. We do not apply in this work the usual duality arguments but explore instead a direct approach in the framework of global Carleman estimates. More precisely, we consider the control that minimizes over the class of admissible null controls a functional involving weighted integrals of the state and the control. The optimality conditions show that both the optimal control and the associated state are expressed in terms of a new variable, the solution of a fourth-order elliptic problem defined in the space-time domain. We first prove that, for some specific weights determined by the global Carleman inequalities for the wave equation, this problem is well-posed. Then, in the framework of the finite element method, we introduce a family of finite-dimensional approximate control problems and we prove a strong convergence result. Numerical experiments confirm the analysis. We complete our study with several comments.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/one-dimensional wave equationnull controllabilityfinite element methodsCarleman estimatesinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1051/cocv/2013046