Convergence of a two-grid algorithm for the control of the wave equation

Ignat LI, Zuazua E (2009)

Publication Type: Journal article

Publication year: 2009

Journal

Journal of the European Mathematical Society European Mathematical Society

Book Volume: 11

Pages Range: 351-391

Journal Issue: 2

Abstract

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.

Authors with CRIS profile

Enrique Zuazua Iriondo

Involved external institutions

Romanian Academy / Academia Română RO Romania (RO) Basque Center of Applied Mathematics (BCAM) ES Spain (ES)

How to cite

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.

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