Summary
The problem of controlling a semi-discrete 1-d wave equation using a multigrid method is studied. The control function acts on the system through the extreme x = 1 of the space interval (0,1). In this lecture we present a proof of a 2-grid algorithm for the numerical approximation of the control, proposed by R. Glowinski [G].
Supported by grant BFM 2001-03345 of the MCYT, Spain
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References
R. Glowinski, Ensuring well posedness by analogy: Stokes problem and boundary control for the wave equation, J. Comput. Physics, 103 (2) (1992), 189–221.
J. A. Infante and E. Zuazua, Boundary observability for the space discretization of the one-dimensional wave equation, M 2 AN, 33 (2) (1999), 407–438.
J.-L. Lions, Contrôlabilité exacte perturbations et stabilisation de systèmes distribués, Vol. 1 and 2, Masson, Paris, (1988).
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© 2003 Springer-Verlag Berlin Heidelberg
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Negreanu, M., Zuazua, E. (2003). A 2-Grid Algorithm for the 1-d Wave Equation. In: Cohen, G.C., Joly, P., Heikkola, E., Neittaanmäki, P. (eds) Mathematical and Numerical Aspects of Wave Propagation WAVES 2003. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55856-6_34
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DOI: https://doi.org/10.1007/978-3-642-55856-6_34
Publisher Name: Springer, Berlin, Heidelberg
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