Global maximum norm parameter-uniform numerical method for a singularly perturbed convection-diffusion problem with discontinuous convection coefficient

Authors:
P. A. Farrell;A. F. Hegarty;J. J. H. Miller;E. O'Riordan;G. I. Shishkin
Affiliations:
-;-;-;-;-
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2004

Citing 1
Cited 5

Singularly perturbed convection-diffusion problems with boundary and weak interior layers

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Abstract

A singularly perturbed convection-diffusion problem, with a discontinuous convection coefficient and a singular perturbation parameter @e, is examined. Due to the discontinuity an interior layer appears in the solution. A finite difference method is constructed for solving this problem, which generates @e-uniformly convergent numerical approximations to the solution. The method uses a piecewise uniform mesh, which is fitted to the interior layer, and the standard upwind finite difference operator on this mesh. The main theoretical result is the @e-uniform convergence in the global maximum norm of the approximations generated by this finite difference method. Numerical results are presented, which are in agreement with the theoretical results.