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An upwind difference scheme on a novel Shishkin-type mesh for a linear convection–diffusion problem

✍ Scribed by Torsten Linß

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
110 KB
Volume
110
Category
Article
ISSN
0377-0427

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✦ Synopsis

We consider an upwind ÿnite di erence scheme on a novel layer-adapted mesh (a modiÿcation of Shishkin's piecewise uniform mesh) for a model singularly perturbed convection-di usion problem in two dimensions. We prove that the upwind scheme on the modiÿed Shishkin mesh is ÿrst-order convergent in the discrete L ∞ norm, independently of the di usion parameter , provided only that the perturbation parameter satisÿes 6N -1 , where O(N 2 ) mesh points are used. The new mesh yields more accurate results than simple upwinding on a standard Shishkin mesh, even though it requires essentially the same computational e ort. Numerical experiments support these theoretical results.

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