Global a priori convergence theory for reduced-basis approximations of single-parameter symmetric coercive elliptic partial differential equations - Archive ouverte HAL Access content directly
Journal Articles Comptes rendus de l'Académie des sciences. Série I, Mathématique Year : 2002

Global a priori convergence theory for reduced-basis approximations of single-parameter symmetric coercive elliptic partial differential equations

Abstract

We consider "Lagrangian" reduced-basis methods for single-parameter symmetric coercive elliptic partial differential equations. We show that, for a logarithmic-(quasi-)uniform distribution of sample points, the reduced-basis approximation converges exponentially to the exact solution uniformly in parameter space. Furthermore, the convergence rate depends only weakly on the continuity-coercivity ratio of the operator: thus very low- dimensional approximations yield accurate solutions even for very wide parametric ranges. Numerical tests (reported elsewhere) corroborate the theoretical preditions.
Fichier principal
Vignette du fichier
CRAS_reduced_basis_turinici_patera_maday.pdf (192.9 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00798389 , version 1 (11-03-2013)

Identifiers

Cite

Yvon Maday, Anthony T. Patera, Gabriel Turinici. Global a priori convergence theory for reduced-basis approximations of single-parameter symmetric coercive elliptic partial differential equations. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2002, 335 (3), pp.289-294. ⟨10.1016/S1631-073X(02)02466-4⟩. ⟨hal-00798389⟩
276 View
408 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More