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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

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

## Abstract

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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