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

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• 作者：Sylvain Ervedoza
• 关键词：Mathematics Subject Classification (2000) 35L05 ; 35L90 ; 65J10 ; 93B07 ; 93B05 ; 93B40 ; 93D15
• 刊名：Numerische Mathematik
• 出版年：2009
• 出版时间：September, 2009
• 年：2009
• 卷：113
• 期：3
• 页码：377-415
• 全文大小：520.7 KB

文摘

In this article, we derive uniform admissibility and observability properties for the finite element space semi-discretizations of [(u)\ddot]+A₀ u=0{\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 [(u)\ddot]+A₀u = 0{\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 [(u)\ddot]+A₀ u=0{\ddot u+A_0 u=0}. We also present applications of our results to controllability and stabilization problems.