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A monotonic evaluation of lower bounds for inf-sup stability constants in the frame of reduced basis approximations

Authors :
Jerónimo Rodríguez
Yanlai Chen
Yvon Maday
Jan S. Hesthaven
Division of Applied Mathematics (DAM)
Brown University
Laboratoire Jacques-Louis Lions (LJLL)
Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)
Propagation des Ondes : Étude Mathématique et Simulation (POEMS)
Inria Saclay - Ile de France
Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Unité de Mathématiques Appliquées (UMA)
École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-Centre National de la Recherche Scientifique (CNRS)
Source :
Comptes Rendus. Mathématique, Comptes Rendus. Mathématique, Académie des sciences (Paris), 2008, 346 (23-24), pp.1295-1300. ⟨10.1016/j.crma.2008.10.012⟩, Comptes Rendus. Mathématique, 2008, 346 (23-24), pp.1295-1300. ⟨10.1016/j.crma.2008.10.012⟩
Publication Year :
2008
Publisher :
HAL CCSD, 2008.

Abstract

For accurate a posteriori error analysis of the reduced basis method for coercive and non-coercive problems, a critical ingredient lies in the evaluation of a lower bound for the coercivity or inf-sup constant. In this short Note, we generalize and improve the successive constraint method first presented by Huynh (2007) by providing a monotonic version of this algorithm that leads to both more stable evaluations and fewer offline computations. To cite this article: Y Chen et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008). (C) 2008 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

Subjects

Subjects :
Basis (linear algebra)
Stability (learning theory)
Monotonic function
010103 numerical & computational mathematics
General Medicine
01 natural sciences
Upper and lower bounds
010101 applied mathematics
Constraint (information theory)
A priori and a posteriori
Applied mathematics
0101 mathematics
Constant (mathematics)
Algorithm
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Numerical stability
Mathematics

Details

Language :
English
ISSN :
1631073X and 17783569
Database :
OpenAIRE
Journal :
Comptes Rendus. Mathématique, Comptes Rendus. Mathématique, Académie des sciences (Paris), 2008, 346 (23-24), pp.1295-1300. ⟨10.1016/j.crma.2008.10.012⟩, Comptes Rendus. Mathématique, 2008, 346 (23-24), pp.1295-1300. ⟨10.1016/j.crma.2008.10.012⟩
Accession number :
edsair.doi.dedup.....277ad2f7ab14f9e3fd748c2557e95193
Full Text :
https://doi.org/10.1016/j.crma.2008.10.012⟩
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