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A note on the stability and accuracy of C n finite elements in steady diffusion‐convection problems
Author(s) -
Okamoto Naotaka,
Niki Hiroshi
Publication year - 1985
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/fld.1650050904
Subject(s) - finite element method , stability (learning theory) , mathematics , convection–diffusion equation , mathematical analysis , steady state (chemistry) , interpolation (computer graphics) , diffusion , convection , mixed finite element method , extended finite element method , function (biology) , thermodynamics , physics , classical mechanics , chemistry , computer science , motion (physics) , machine learning , evolutionary biology , biology
The paper is concerned with stability and accuracy of an n th order Lagrangian family of finite element steady‐state solutions of the diffusion‐convection equation, and furthermore is concerned with the stability and the accuracy of on m th kind Hermitian family of finite element solutions. We discuss the stability of the numerical solution based on the fact that the characteristic finite element solution can be expressed approximately as a rational function of cell Peclet number Pe c ( = uh / k ). Moreover, it is shown that by eliminating derivatives and by using the interpolation method over elements a stable solution is obtained over the domain independent of Pe c for P 1,3 , and for P 2,5 the stable solution is obtained for Pe c less than 44.4.