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Boundary observability for the space-discretizations of the 1-d wave equation



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Infante del Río, Juan Antonio and Zuazua Iriondo, Enrique (1998) Boundary observability for the space-discretizations of the 1-d wave equation. Comptes Rendus de l'Académie des Sciences. Série I. Mathématique, 326 (6). pp. 713-718. ISSN 0764-4442

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Official URL: http://www.sciencedirect.com/science/article/pii/S0764444298800360


We consider the finite-difference and finite-element space discretization of the 1 - d wave equation with homogeneous Dirichlet boundary conditions in a bounded interval. We analyze the problem of estimating the total energy of solutions in terms of the energy concentrated on the boundary, uniformly as the net-spacing h --> 0. We prove that there is no such a uniform bound due to spurious high frequencies. We prove however an uniform bound in suitable subspaces of solutions that eventually cover the whole energy space.

Item Type:Article
Subjects:Sciences > Physics > Mathematical physics
ID Code:23308
Deposited On:22 Oct 2013 10:24
Last Modified:12 Dec 2018 15:07

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