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Adequacy of finite difference schemes for convection‐diffusion equations
Author(s) -
Shapira Yair
Publication year - 2002
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.10007
Subject(s) - mathematics , limit (mathematics) , a priori and a posteriori , finite difference , partial differential equation , boundary value problem , finite difference method , diffusion , convection–diffusion equation , viscosity , boundary layer , convection , finite difference scheme , zero (linguistics) , viscosity solution , mathematical analysis , mechanics , thermodynamics , physics , philosophy , linguistics , epistemology
Finite difference schemes for the numerical solution of singularly perturbed convection problems on uniform grids are studied in the limit case where the viscosity and the meshsize approach zero at the same time. The present error estimates are given in terms of order of magnitude in the above limit process and are useful in a priori choosing adequate schemes and meshsizes for boundary‐layer problems and problems with closed characteristics. Published 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 280–295, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/num.10007