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An upwind finite‐volume element scheme and its maximum‐principle‐preserving property for nonlinear convection–diffusion problem
Author(s) -
Gao Fuzheng,
Yuan Yirang,
Yang Danping
Publication year - 2007
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.1623
Subject(s) - upwind scheme , mathematics , finite volume method , nonlinear system , finite element method , convection–diffusion equation , maximum principle , norm (philosophy) , scheme (mathematics) , convection , mathematical analysis , mathematical optimization , mechanics , physics , law , optimal control , quantum mechanics , political science , discretization , thermodynamics
For a class of nonlinear convection–diffusion equation in multiple space dimensions, a kind of upwind finite‐volume element (UFVE) scheme is put forward. Some techniques, such as calculus of variations, commutating operators and prior estimates, are adopted. It is proved that the UFVE scheme is unconditionally stable and satisfies maximum principle. Optimal‐order estimates in H 1 ‐norm are derived to determine the error in the approximate solution. Numerical results are presented to observe the performance of the scheme. Copyright © 2007 John Wiley & Sons, Ltd.