Convergence rates for the quasi-reversibility method to solve the Cauchy problem for Laplace's equation

Laurent Bourgeois 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : We consider the quasi-reversibility method to solve the Cauchy problem for Laplace's equation in a smooth bounded domain. We assume that the Cauchy data are contaminated by some noise of amplitude σ, so that we make a regular choice of ε as a function of σ, where ε is the small parameter of the quasi-reversibility method. Specifically, we present two different results concerning the convergence rate of the solution of quasi-reversibility to the exact solution when σ tends to 0. The first result is a convergence rate of type 1\big/\big(\log{\frac{1}{{{\sigma}}}}\big)^\beta in a truncated domain, the second one holds when a source condition is assumed and is a convergence rate of type {{\sigma}}^{\frac{1}{2}} in the whole domain. © 2006 IOP Publishing Ltd.
Type de document :
Article dans une revue
Inverse Problems, IOP Publishing, 2006, 22 (2), pp.413-430. 〈10.1088/0266-5611/22/2/002〉
Liste complète des métadonnées

https://hal-ensta.archives-ouvertes.fr/hal-00876239
Contributeur : Aurélien Arnoux <>
Soumis le : jeudi 31 octobre 2013 - 17:05:47
Dernière modification le : jeudi 11 janvier 2018 - 06:20:23

Lien texte intégral

Identifiants

Collections

Citation

Laurent Bourgeois. Convergence rates for the quasi-reversibility method to solve the Cauchy problem for Laplace's equation. Inverse Problems, IOP Publishing, 2006, 22 (2), pp.413-430. 〈10.1088/0266-5611/22/2/002〉. 〈hal-00876239〉

Partager

Métriques

Consultations de la notice

140