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Uniform pointwise convergence of difference schemes for convection-diffusion problems on layer-adapted meshes

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posted on 2017-05-04, 11:01 authored by Natalia KoptevaNatalia Kopteva
We consider two convection-diffusion boundary value problems in conservative form: for an ordinary differential equation and for a parabolic equation. Both the problems are discretized using a four-point second-order upwind space difference operator on arbitrary and layer-adapted space meshes. We give ɛ-uniform maximum norm error estimates O(N−2ln2N(+τ)) and O(N−2(+τ)), respectively, for the Shishkin and Bakhvalov space meshes, where N is the space meshnodes number, τ is the time meshinterval. The smoothness condition for the Bakhvalov mesh is replaced by a weaker condition.

History

Publication

Computing;66 (2), pp. 179-197

Publisher

Springer

Note

peer-reviewed

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The original publication is available at www.springerlink.com

Language

English

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