ACCURATE DISCRETIZATION FOR SINGULAR PERTURBATIONS - THE ONE-DIMENSIONAL CASE

Authors
HU XC MANTEUFFEL TA MCCORMICK S RUSSELL TF
Citation
Xc. Hu et al., ACCURATE DISCRETIZATION FOR SINGULAR PERTURBATIONS - THE ONE-DIMENSIONAL CASE, SIAM journal on numerical analysis, 32(1), 1995, pp. 83-109
Citations number
19
Categorie Soggetti
Mathematics,Mathematics
Journal title
SIAM journal on numerical analysis → ACNP
ISSN journal
00361429
Volume
32
Issue
1
Year of publication
1995
Pages
83 - 109
Database
ISI
SICI code
0036-1429(1995)32:1<83:ADFSP->2.0.ZU;2-C
Abstract
This paper develops a discretization method for one-dimensional singul ar perturbation problems based on a Petrov-Galerkin finite element, or an equivalent finite volume, scheme. The method is unique in that (1) its discretization error has a bound that is second order in the mesh size and uniform in the perturbation parameter; (2) it satisfies a lo cal discrete conservation law; (3) and it exhibits a discrete maximum principle. Numerical results are included for comparison with the theo ry.