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A note on second‐order finite‐difference schemes on uniform meshes for advection‐‐diffusion equations
Author(s) -
Funaro Daniele
Publication year - 1999
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/(sici)1098-2426(199909)15:5<581::aid-num5>3.0.co;2-m
Subject(s) - mathematics , advection , generalization , polygon mesh , partial differential equation , finite difference method , diffusion , viscosity , finite difference , order (exchange) , scheme (mathematics) , partial derivative , mathematical analysis , geometry , economics , thermodynamics , quantum mechanics , physics , finance
An artificial‐viscosity finite‐difference scheme is introduced for stabilizing the solutions of advection‐diffusion equations. Although only the linear one‐dimensional case is discussed, the method is easily susceptible to generalization. Some theory and comparisons with other well‐known schemes are carried out. The aim is, however, to explain the construction of the method, rather than considering sophisticated applications. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 581–588, 1999