Numerical solution of a convection diffusion problem with Robin boundary conditions

Authors:
Ali R. Ansari;Alan F. Hegarty
Affiliations:
Department of Mathematics & Statistics, College of Informatics & Electronics, University of Limerick, Limerick, Ireland;Department of Mathematics & Statistics, College of Informatics & Electronics, University of Limerick, Limerick, Ireland
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

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Abstract

We consider a one-dimensional steady-state convection dominated convection-diffusion problem with Robin boundary conditions. We show, both theoretically and with numerical experiments, that numerical solutions obtained using an upwind finite difference scheme on Shishkin meshes are uniformly convergent with respect to the diffusion coefficient.