Error analysis of an equation error method for the identification of the diffusion coefficient in a quasi-linear parabolic differential equation

Citation
M. Hanke et O. Scherzer, Error analysis of an equation error method for the identification of the diffusion coefficient in a quasi-linear parabolic differential equation, SIAM J A MA, 59(3), 1999, pp. 1012-1027
Citations number
21
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mathematics
Journal title
SIAM JOURNAL ON APPLIED MATHEMATICS
ISSN journal
0036-1399 → ACNP
Volume
59
Issue
3
Year of publication
1999
Pages
1012 - 1027
Database
ISI
SICI code
0036-1399(19990323)59:3<1012:EAOAEE>2.0.ZU;2-Z
Abstract
We consider the inverse problem of reconstructing the diffusion coefficient in a quasi-linear parabolic differential equation in divergence form from measurements of the solution at a finite number of points in the interior o f the domain. An equation error method is developed which transforms the in verse problem into a system of linear operator equations for the diffusion coefficient and which can be solved by the conjugate gradient method in a v ery efficient and stable manner. A detailed error analysis relates the requ ired number of measurements with their accuracy. Numerical results illustra te the performance of the method.