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The streamline–diffusion method for a convection–diffusion problem with a point source
Author(s) -
Roos Hans–Görg,
Zarin Helena
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310229
Subject(s) - superconvergence , convection–diffusion equation , mathematics , polygon mesh , diffusion , norm (philosophy) , convergence (economics) , finite element method , convection , uniform convergence , mathematical analysis , mathematical optimization , geometry , computer science , mechanics , physics , computer network , bandwidth (computing) , political science , law , economics , thermodynamics , economic growth
A linear singularly perturbed convection–diffusion problem with a point source is considered. The problem is solved using the streamline–diffusion finite element method on a class of Shishkin–type meshes. We prove that the method is almost optimal with uniform second order of convergence in the maximum norm. We also prove the existence of superconvergent points for the first derivative. Numerical experiments support these theoretical results.