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The ε‐Uniform Convergence of a Defect‐Correction Method on a Shishkin Mesh
Author(s) -
Fróhner A.,
Linss T.,
Roos H.G.
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.200108115153
Subject(s) - mathematics , uniform convergence , convergence (economics) , norm (philosophy) , finite difference method , upwind scheme , finite difference , finite difference scheme , mathematical analysis , boundary value problem , perturbation (astronomy) , computer science , discretization , computer network , physics , bandwidth (computing) , quantum mechanics , political science , law , economics , economic growth
Abstract A defect correction method based on finite difference schemes is considered for a singularly perturbed boundary value problem on a Shishkin mesh. The method combines the stability of the upwind difference scheme and the higher‐order accuracy of the central difference scheme. The almost second‐order convergence of the scheme with respect to the discrete maximum norm, uniformly in the perturbation parameter ε, is proved. Numerical experiments support the theoretical results.