Approximation of the bifurcation function for elliptic boundary value problems

Authors
Smiley, MW Chun, C
Citation
Mw. Smiley et C. Chun, Approximation of the bifurcation function for elliptic boundary value problems, NUMER M P D, 16(2), 2000, pp. 194-213
Citations number
19
Categorie Soggetti
Engineering Mathematics
Journal title
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
ISSN journal
0749159X → ACNP
Volume
16
Issue
2
Year of publication
2000
Pages
194 - 213
Database
ISI
SICI code
0749-159X(200003)16:2<194:AOTBFF>2.0.ZU;2-K
Abstract
The bifurcation function for an elliptic boundary value problem is a vector field B(omega) on R-d whose zeros an in a one-to-one correspondence with t he solutions of the boundary value problem. Finite element approximations o f the boundary value problem are shown to give rise to an approximate bifur cation function B-h(omega), which is also a vector field on R-d. Estimates of the difference B(omega) - B-h(omega) are derived, and methods for comput ing B-h(omega) are discussed. (C) 2000 John Wiley & Sons, Inc.