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FINITE ELEMENT RESOLUTION OF CONVECTION–DIFFUSION EQUATIONS WITH INTERIOR AND BOUNDARY LAYERS
Author(s) -
OLMOS F.,
CHINESTA F.,
TORRES R.
Publication year - 1996
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/(sici)1097-0363(19960415)22:7<643::aid-fld372>3.0.co;2-u
Subject(s) - finite element method , mathematics , polynomial , convection–diffusion equation , mathematical analysis , resolution (logic) , spectral element method , boundary (topology) , exponential function , boundary knot method , boundary value problem , laminar flow , diffusion , extended finite element method , boundary element method , geometry , physics , computer science , mechanics , artificial intelligence , thermodynamics
The purpose of this paper is to present a new algorithm for the resolution of both interior and boundary layers present in the convection–diffusion equation in laminar regimes, based on the formulation of a family of polynomial– exponential elements. We have carried out an adaptation of the standard variational methods (finite element method and spectral element method), obtaining an algorithm which supplies non‐oscillatory and accurate solutions. The algorithm consists of generating a coupled grid of polynomial standard elements and polynomial–exponential elements. The latter are able to represent the high gradients of the solution, while the standard elements represent the solution in the areas of smooth variation.