An Ingham type proof for a two-grid observability theorem
Résumé
Here, we prove the uniform observability of a two-grid method for the semi-discretization of the 1D-wave equation for a time
$t>2\sqrt{2}$; this time, if the observation is made in $(-T/2,T/2)$, is optimal and this result improves an earlier work of Negreanu and Zuazua [C. R. Acad. Sci. Paris Sér. I 338 (2004) 413–418]. Our proof follows an Ingham type approach.