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The effect of group velocity in the numerical analysis of control problems for the wave equation. (English) Zbl 1048.93047

Cohen, Gary C. (ed.) et al., Mathematical and numerical aspects of wave propagation, WAVES 2003. Proceedings of the sixth international conference on mathematical and numerical aspects of wave propagation, Jyväskylä, Finland, 30 June – 4 July 2003. Berlin: Springer (ISBN 3-540-40127-X/hbk). 195-200 (2003).
Based on the theory developed by F. Macià Lang [Propagación y control de vibraciones en medios discretos y continuous, Ph. D. Thesis, Universidad Complutense de Madrid, 2002], associated to discrete functions Wigner measures, an algorithm for the numerical computation of interior controls for the wave equation is suggested. This algorithm’s convergence depends on the group velocity of the numerical scheme used to discretize the wave equation. Some results on the convergence of partial controls are given.
For the entire collection see [Zbl 1029.00072].

MSC:

93C20 Control/observation systems governed by partial differential equations
93B40 Computational methods in systems theory (MSC2010)
35L05 Wave equation
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