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A finite element method for two–parameter singularly perturbed problems in 2D
Author(s) -
Teofanov Ljiljana,
Roos HansGörg,
Zarin Helena
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610366
Subject(s) - finite element method , mathematics , piecewise , norm (philosophy) , singular perturbation , bilinear interpolation , convergence (economics) , square (algebra) , bilinear form , mathematical analysis , mixed finite element method , unit square , geometry , physics , statistics , law , economics , economic growth , thermodynamics , political science
We consider a singularly perturbed elliptic problem with two small parameters posed on the unit square. Based on a decomposition of the solution, we prove uniform convergence of a finite element method in an energy norm. The method uses piecewise bilinear functions on a layer‐adapted Shishkin mesh. Numerical results confirm our theoretical analysis. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)