Abstract
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 −2ln2 N(+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.
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Received December 14, 1999; revised September 13, 2000
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Kopteva, N. Uniform Pointwise Convergence of Difference Schemes for Convection-Diffusion Problems on Layer-Adapted Meshes. Computing 66, 179–197 (2001). https://doi.org/10.1007/s006070170034
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DOI: https://doi.org/10.1007/s006070170034