TY - JOUR
T1 - Global maximum norm parameter-uniform numerical method for a singularly perturbed convection-diffusion problem with discontinuous convection coefficient
AU - Farrell, P. A.
AU - Hegarty, A. F.
AU - Miller, J. J.H.
AU - O'Riordan, E.
AU - Shishkin, G. I.
PY - 2004/12
Y1 - 2004/12
N2 - A singularly perturbed convection-diffusion problem, with a discontinuous convection coefficient and a singular perturbation parameter ε, 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 ε-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 ε-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.
AB - A singularly perturbed convection-diffusion problem, with a discontinuous convection coefficient and a singular perturbation parameter ε, 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 ε-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 ε-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.
KW - Difference scheme
KW - Discontinuous coefficient
KW - Interior layer
KW - Piecewise-uniform mesh
KW - Singularly perturbed ODE
UR - http://www.scopus.com/inward/record.url?scp=18044373276&partnerID=8YFLogxK
U2 - 10.1016/j.mcm.2005.01.025
DO - 10.1016/j.mcm.2005.01.025
M3 - Article
AN - SCOPUS:18044373276
SN - 0895-7177
VL - 40
SP - 1375
EP - 1392
JO - Mathematical and Computer Modelling
JF - Mathematical and Computer Modelling
IS - 11-12
ER -