Ignat LI, Zuazua E (2009)
Publication Type: Journal article
Publication year: 2009
Book Volume: 11
Pages Range: 351-391
Journal Issue: 2
We analyze the problem of boundary observability of the finite-difference space semidiscretizations of the 2-d wave equation in the square. We prove the uniform (with respect to the mesh-size) boundary observability for the solutions obtained by the two-grid preconditioner introduced by Glowinski [9]. Our method uses previously known uniform observability inequalities for low frequency solutions and a dyadic spectral time decomposition. As a consequence we prove the convergence of the two-grid algorithm for computing the boundary controls for the wave equation. The method can be applied in any space dimension, for more general domains and other discretization schemes.
APA:
Ignat, L.I., & Zuazua, E. (2009). Convergence of a two-grid algorithm for the control of the wave equation. Journal of the European Mathematical Society, 11(2), 351-391.
MLA:
Ignat, Liviu I., and Enrique Zuazua. "Convergence of a two-grid algorithm for the control of the wave equation." Journal of the European Mathematical Society 11.2 (2009): 351-391.
BibTeX: Download