| Issue |
ESAIM: COCV
Volume 14, Number 3, July-September 2008
|
|
|---|---|---|
| Page(s) | 604 - 631 | |
| DOI | https://doi.org/10.1051/cocv:2007062 | |
| Published online | 21 December 2007 | |
An Ingham type proof for a two-grid observability theorem
1
Dipartimento di Metodi e Modelli Matematici
per le Scienze Applicate, Sapienza Università di Roma,
Via A. Scarpa 16, 00161 Roma, Italy; loreti@dmmm.uniroma1.it
2
IRMA, Université Louis Pasteur,
7 rue René Descartes,
67084 Strasbourg, France; mehrenbe@math.u-strasbg.fr
Received:
11
July
2005
Revised:
10
February
2006
Revised:
26
April
2006
Here, we prove the uniform observability of a two-grid method
for the semi-discretization of the 1D-wave equation for a time 
;
this time, if the observation is made in 
, 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.
Mathematics Subject Classification: 35L05 / 65M55 / 93B07
Key words: Uniform observability / two-grid method / Ingham type theorem
© EDP Sciences, SMAI, 2007
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