A global uniformly convergent finite element method for a quasi-linear singularly perturbed elliptic problem

Authors
Li, JC Navon, IM
Citation
Jc. Li et Im. Navon, A global uniformly convergent finite element method for a quasi-linear singularly perturbed elliptic problem, COMPUT MATH, 38(5-6), 1999, pp. 197-206
Citations number
34
Categorie Soggetti
Computer Science & Engineering
Journal title
COMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN journal
08981221 → ACNP
Volume
38
Issue
5-6
Year of publication
1999
Pages
197 - 206
Database
ISI
SICI code
0898-1221(199909)38:5-6<197:AGUCFE>2.0.ZU;2-Y
Abstract
In this paper, we construct a bilinear finite element method based on a spe cial piecewise uniform mesh for solving a quasi-linear singularly perturbed elliptic problem in two space dimensions. A quasi-optimal global uniform c onvergence rate O(N-x(-2) ln(2) N-x + N-y(-2) ln(2) N-y) was obtained, whic h is independent of the perturbation parameter. Here N-x and N-y are the nu mber of elements in the x-and y-directions, respectively. (C) 1999 Elsevier Science Ltd. All rights reserved.