Spectral conditions for admissibility and observability of wave systems: applications to finite element schemes |
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Authors: | Sylvain Ervedoza |
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Institution: | (1) Laboratoire de Mathématiques de Versailles, Université de Versailles Saint-Quentin-en-Yvelines, 45 avenue des états Unis, 78035 Versailles Cedex, France |
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Abstract: | In this article, we derive uniform admissibility and observability properties for the finite element space semi-discretizations
of , 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 , 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 . We also present applications of our results to controllability and stabilization problems.
The author was partially supported by the “Agence Nationale de la Recherche” (ANR), Project C-QUID, number BLAN-3-139579. |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 35L05 35L90 65J10 93B07 93B05 93B40 93D15 |
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