Abstract
In this paper we discuss the numerical implementation of a systematic method for the exact boundary controllability of the wave equation, concentrating on the particular case of Dirichlet controls. The numerical methods described here consist in a combination of: finite element approximations for the space discretization; explicit finite difference schemes for the time discretization; a preconditioned conjugate gradient algorithm for the solution of the discrete problems; a pre/post processing technique based on a biharmonic Tychonoff regularization. The efficiency of the computational methodology is illustrated by the results of numerical experiments.
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Dedicated to Jim Douglas for his 60th Birthday
An erratum to this article is available at http://dx.doi.org/10.1007/BF03167859.
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Glowinski, R., Li, CH. & Lions, JL. A numerical approach to the exact boundary controllability of the wave equation (I) Dirichlet controls: Description of the numerical methods. Japan J. Appl. Math. 7, 1–76 (1990). https://doi.org/10.1007/BF03167891
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DOI: https://doi.org/10.1007/BF03167891