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 ε-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 mesh-interval. The smoothness condition for the Bakhvalov mesh is replaced by a weaker condition.
Original language | English |
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Pages (from-to) | 179-197 |
Number of pages | 19 |
Journal | Computing (Vienna/New York) |
Volume | 66 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2001 |
Keywords
- Bakhvalov mesh
- Convection-diffusion problems
- Four-point upwind difference scheme
- Shishkin mesh
- Singular perturbation