Geodesic
Convergence of a two-grid algorithm for the control of the wave equation
Journal of the European Mathematical Society, Tome 11 (2009) no. 2, pp. 351-391 Cet article a éte moissonné depuis la source EMS Press

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We analyze the problem of boundary observability of the finite-difference space semi-discretizations 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.
DOI : 10.4171/jems/153
Classification : 35-XX, 65-XX, 93-XX, 00-XX
Keywords: Waves, finite difference approximation, propagation, observation, control, two-grid 
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     author = {Liviu I. Ignat and Enrique Zuazua},
     title = {Convergence of a two-grid algorithm for the control of the wave equation},
     journal = {Journal of the European Mathematical Society},
     pages = {351--391},
     year = {2009},
     volume = {11},
     number = {2},
     doi = {10.4171/jems/153},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/153/}
}
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Liviu I. Ignat; Enrique Zuazua. Convergence of a two-grid algorithm for the control of the wave equation. Journal of the European Mathematical Society, Tome 11 (2009) no. 2, pp. 351-391. doi: 10.4171/jems/153

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