Micu, Sorin Uniform boundary controllability of a semidiscrete 1-D wave equation with vanishing viscosity. (English) Zbl 1176.93017 SIAM J. Control Optim. 47, No. 6, 2857-2885 (2008). Summary: This article deals with the approximation of the boundary control of the linear one-dimensional wave equation. It is known that the high frequency spurious oscillations introduced in the classical methods of finite difference and finite element lead to nonuniform controllability properties (see [J. A. Infante and E. Zuazua, \(M2AN\) Math. Model. Numer. Anal. 33, 407–438 (1999; Zbl 0947.65101)]. A space-discrete scheme with an added numerical vanishing viscous term is presented and analyzed. The extra numerical damping filters out the high numerical frequencies and ensures the convergence of the sequence of discrete controls to a control of the continuous conservative wave equation when the mesh size tends to zero. Cited in 17 Documents MSC: 93B05 Controllability 93B40 Computational methods in systems theory (MSC2010) 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 35L05 Wave equation Keywords:control; wave equation; semidiscrete approximation; numerical viscosity Citations:Zbl 0947.65101 PDFBibTeX XMLCite \textit{S. Micu}, SIAM J. Control Optim. 47, No. 6, 2857--2885 (2008; Zbl 1176.93017) Full Text: DOI Link