Uniform convergence and mesh independence of Newton's method for discretized variational problems

Citation
Al. Dontchev et al., Uniform convergence and mesh independence of Newton's method for discretized variational problems, SIAM J CON, 39(3), 2000, pp. 961-980
Citations number
14
Categorie Soggetti
Mathematics,"Engineering Mathematics
Journal title
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
ISSN journal
03630129 → ACNP
Volume
39
Issue
3
Year of publication
2000
Pages
961 - 980
Database
ISI
SICI code
0363-0129(20001023)39:3<961:UCAMIO>2.0.ZU;2-Q
Abstract
In an abstract framework, we study local convergence properties of Newton's method for a sequence of generalized equations which models a discretized variational inequality. We identify conditions under which the method is lo cally quadratically convergent, uniformly in the discretization. Moreover, we show that the distance between the Newton sequence for the continuous pr oblem and the Newton sequence for the discretized problem is bounded by the norm of a residual. As an application, we present mesh-independence result s for an optimal control problem with control constraints.