Peer-Reviewed Journal Details
Mandatory Fields
Farrell, PA; Hegarty, AF; Miller, JJH; O'Riordan, E; Shishkin, GI
2004
December
Mathematical And Computer Modelling
Global maximum norm parameter-uniform numerical method for a singularly perturbed convection-diffusion problem with discontinuous convection coefficient
Published
()
Optional Fields
singularly perturbed ODE discontinuous coefficient interior layer difference scheme piecewise-uniform mesh
40
11-12
1375
1392
A singularly perturbed convection-diffusion problem, with a discontinuous convection coefficient and a singular perturbation parameter c, 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 approximatioris generated by this finite difference method. Numerical results are presented, which are in agreement with the theoretical results. (C) 2005 Elsevier Ltd. All rights reserved.
0895-7177
10.1016/j.mcm.2005.01.025
Grant Details