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Castro Barbero, Carlos Manuel and Micu, Sorín and Münch, Arnaud (2008). Numerical approximation of the boundary control for the wave equation with mixed finite elements in a square. "Ima Journal of Numerical Analysis", v. 28 (n. 1); pp. 186-214. ISSN 0272-4979. https://doi.org/10.1093/imanum/drm012.
Title: | Numerical approximation of the boundary control for the wave equation with mixed finite elements in a square |
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Author/s: |
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Item Type: | Article |
Título de Revista/Publicación: | Ima Journal of Numerical Analysis |
Date: | January 2008 |
ISSN: | 0272-4979 |
Volume: | 28 |
Subjects: | |
Freetext Keywords: | exact controllability; observability; numerical approximation of controls; wave equation |
Faculty: | E.T.S.I. Caminos, Canales y Puertos (UPM) |
Department: | Matemática e Informática Aplicadas a la Ingeniería Civil [hasta 2014] |
Creative Commons Licenses: | Recognition - No derivative works - Non commercial |
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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.
Item ID: | 2922 |
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DC Identifier: | https://oa.upm.es/2922/ |
OAI Identifier: | oai:oa.upm.es:2922 |
DOI: | 10.1093/imanum/drm012 |
Official URL: | http://imajna.oxfordjournals.org/content/vol28/iss... |
Deposited by: | Memoria Investigacion |
Deposited on: | 14 May 2010 11:45 |
Last Modified: | 20 Apr 2016 12:32 |