2023-03-20T18:26:00Z
https://oa.upm.es/cgi/oai2
oai:oa.upm.es:2922
2016-04-20T12:32:52Z
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747970653D61727469636C65
Numerical approximation of the boundary control for the wave equation with mixed finite elements in a square
Castro Barbero, Carlos Manuel
Micu, Sorín
Münch, Arnaud
Mathematics
This paper studies the numerical approximation of the boundary control for the wave equation in a square domain. It is known that the discrete and semi-discrete models ob- tained by discretizing the wave equation with the usual ¯nite di®erence or ¯nite element methods do not provide convergent sequences of approximations to the boundary control of the continuous wave equation, as the mesh size goes to zero (see [7, 15]). Here we introduce and analyze a new semi-discrete model based on the space discretization of the wave equa- tion using a mixed ¯nite element method with two di®erent basis functions for the position and velocity. The main theoretical result is a uniform observability inequality which allows us to construct a sequence of approximations converging to the minimal L2¡norm control of the continuous wave equation. We also introduce a fully-discrete system, obtained from our semi-discrete scheme, for which we conjecture that it provides a convergent sequence of discrete approximations as both h and ¢t, the time discretization parameter, go to zero. We illustrate this fact with several numerical experiments.
E.T.S.I. Caminos, Canales y Puertos (UPM)
https://creativecommons.org/licenses/by-nc-nd/3.0/es/
2008-01
info:eu-repo/semantics/article
Article
Ima Journal of Numerical Analysis, ISSN 0272-4979, 2008-01, Vol. 28, No. 1
PeerReviewed
application/pdf
eng
http://imajna.oxfordjournals.org/content/vol28/issue1/index.dtl
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/altIdentifier/doi/10.1093/imanum/drm012
https://oa.upm.es/2922/