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

Journal of the European Mathematical Society (2009)

- Volume: 011, Issue: 2, page 351-391
- ISSN: 1435-9855

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topIgnat, Liviu, and Zuazua, Enrique. "Convergence of a two-grid algorithm for the control of the wave equation." Journal of the European Mathematical Society 011.2 (2009): 351-391. <http://eudml.org/doc/277222>.

@article{Ignat2009,

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 meshsize)
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.},

author = {Ignat, Liviu, Zuazua, Enrique},

journal = {Journal of the European Mathematical Society},

keywords = {waves; finite difference approximation; propagation; observation; control; two-grid; waves; finite difference approximation; propagation; observation; control; two-grid preconditioner},

language = {eng},

number = {2},

pages = {351-391},

publisher = {European Mathematical Society Publishing House},

title = {Convergence of a two-grid algorithm for the control of the wave equation},

url = {http://eudml.org/doc/277222},

volume = {011},

year = {2009},

}

TY - JOUR

AU - Ignat, Liviu

AU - Zuazua, Enrique

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

JO - Journal of the European Mathematical Society

PY - 2009

PB - European Mathematical Society Publishing House

VL - 011

IS - 2

SP - 351

EP - 391

AB - 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 meshsize)
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.

LA - eng

KW - waves; finite difference approximation; propagation; observation; control; two-grid; waves; finite difference approximation; propagation; observation; control; two-grid preconditioner

UR - http://eudml.org/doc/277222

ER -

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