On a set of singularly perturbed convection-diffusion equations

Authors:
Torsten Linß
Affiliations:
TU Dresden, Institut f. Numerische Mathematik, 01062 Dresden, Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

Citing 4
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Sufficient conditions for uniform convergence on layer-adapted grids

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A parameter robust numerical method for a system of two singularly perturbed convection-diffusion equations

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Abstract

We study convergence properties of a first-order upwind difference scheme applied to a weakly coupled system of singularly perturbed convection-diffusion equations. We derive a priori and a posteriori error estimates that are robust with respect to the perturbation parameters. Thereby strengthening and generalising recent results (Appl. Numer. Math. 51 (2004) 171; in: A. Ansari, A Hegarty, G.I. Shishkin, Numerical Methods for Problems with Layer Phenomena, Limerick, 2004, pp. 33-39). The key ingredient of our analysis are strong negative-norm stability results obtained earlier by Andreev (Differential Equations 37(7) (2001) 923) and by Andreev and Kopteva (Differential Equations 34(7) (1998) 921)).