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Uniform pointwise convergence of finite difference schemes for quasilinear convection‐diffusion problems
Author(s) -
Torsten Linss
Publication year - 2001
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200108115146
Subject(s) - pointwise convergence , discretization , mathematics , uniform convergence , pointwise , mathematical analysis , rate of convergence , norm (philosophy) , perturbation (astronomy) , convergence (economics) , boundary value problem , computer science , physics , bandwidth (computing) , channel (broadcasting) , computer network , approx , quantum mechanics , political science , law , economics , economic growth , operating system
We study convergence properties of an upwind difference scheme on layer‐adapted grids for the discretization of a class of singularly perturbed quasilinear two‐point boundary value problems. We derive conditions that are sufficient for uniform convergence in the maximum norm, with respect to the perturbation parameter, of the method. These conditions are easy to check and enable one to immediately deduce the rate of uniform convergence.