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

Ignat, 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 -