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Numerische Mathematik

, Volume 113, Issue 3, pp 377–415 | Cite as

Spectral conditions for admissibility and observability of wave systems: applications to finite element schemes

  • Sylvain Ervedoza
Article

Abstract

In this article, we derive uniform admissibility and observability properties for the finite element space semi-discretizations of \({\ddot u+A_0 u=0 }\), where A 0 is an unbounded self-adjoint positive definite operator with compact resolvent. To address this problem, we present a new spectral approach based on several spectral criteria for admissibility and observability of such systems. Our approach provides very general admissibility and observability results for finite element approximation schemes of \({\ddot u+A_{0}u =0}\), which stand in any dimension and for any regular mesh (in the sense of finite elements). Our results can be combined with previous works to derive admissibility and observability properties for full discretizations of \({\ddot u+A_0 u=0}\). We also present applications of our results to controllability and stabilization problems.

Mathematics Subject Classification (2000)

35L05 35L90 65J10 93B07 93B05 93B40 93D15 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques de VersaillesUniversité de Versailles Saint-Quentin-en-YvelinesVersailles CedexFrance

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