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Uniform boundary controllability of a discrete 1-D wave equation. (English) Zbl 1157.93324
Summary: A numerical scheme for the controlled discrete 1-D wave equation is considered. We prove the convergence of the boundary controls of the discrete equations to a control of the continuous wave equation when the mesh size tends to zero when time and space steps coincide. This positive result is in contrast with previous negative ones for space semi-discretizations.

93C20Control systems governed by PDE
Full Text: DOI
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[2] Isaacson, E.; Keller, H. B.: Analysis of numerical methods. (1966) · Zbl 0168.13101
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[4] S. Micu, Uniform boundary controllability of a semi-discrete 1-D wave equation, Numer. Math. 91 (4) (2002) 723--768. · Zbl 1002.65072
[5] Strauss, W.; Vazquez, L.: Numerical solution of a nonlinear Klein-Gordon equation. J. comput. Phys. 28, No. 2, 271-278 (1978) · Zbl 0387.65076