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A new combined finite element‐upwind finite volume method for convection‐dominated diffusion problems
Author(s) -
Wang Cheng,
He Mingyan,
Sun Pengtao
Publication year - 2016
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22027
Subject(s) - finite volume method , mathematics , upwind scheme , finite element method , convection–diffusion equation , numerical diffusion , numerical solution of the convection–diffusion equation , mixed finite element method , convergence (economics) , mathematical analysis , stability (learning theory) , finite volume method for one dimensional steady state diffusion , convection , partial differential equation , mechanics , numerical partial differential equations , computer science , physics , thermodynamics , machine learning , discretization , economics , economic growth
In this article, we develop a combined finite element‐weighted upwind finite volume method for convection‐dominated diffusion problems in two dimensions, which discretizes the diffusion term with the standard finite element scheme, and the convection and source terms with the weighted upwind finite volume scheme. The developed method leads to a totally new scheme for convection‐dominated problems, which overcomes numerical oscillation, avoids numerical dispersion, and has high‐order accuracy. Stability analyses of the scheme are given for the problems with constant coefficients. Numerical experiments are presented to illustrate the stability and optimal convergence of our proposed method. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 799–818, 2016