Uniform Pointwise Convergence on Shishkin-Type Meshes for Quasi-Linear Convection-Diffusion Problems

Authors:
Torsten Linss;Hans-Görg Roos;Relja Vulanovic
Affiliations:
-;-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2000

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Abstract

A singularly perturbed quasi-linear two-point boundary value problem with an exponential boundary layer is considered. The problem is discretized using a nonstandard upwinded first-order difference scheme on generalized Shishkin-type meshes. We give a uniform error estimate in a discrete $L_\infty$ norm. Numerical experiments support the theoretical results.