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The ε‐Uniform Convergence of a Defect‐Correction Method on a Shishkin Mesh
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2001AbstractA 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.
A. Fróhner, T. Linss, H.‐G. Roos
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A streamline diffusion finite element method on a shishkin mesh for a convection-diffusion problem
Rendiconti del Seminario Matematico e Fisico di Milano, 1994A model of the time-dependent convection-diffusion problem whose solution may exhibit interior and boundary layers is considered. The standard streamline diffusion scheme, with piecewise linear elements on a uniform mesh for such a problem is convergent only at points that are not close to any layer. The main of the paper is to replace the uniform mesh
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Finite element method on Shishkin mesh for a singularly perturbed problem with an interior layer
Applied Mathematics Letters, 2021Jin Zhang, Xiaoqi Ma, Yanhui Lv
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