TY - JOUR
T1 - A parameter-uniform Schwarz method for a singularly perturbed reaction-diffusion problem with an interior layer
AU - Miller, J.J.H.
AU - O'Riordan, E.
AU - Shishkin, G.I.
AU - Wang, Song
PY - 2000
Y1 - 2000
N2 - In this paper we consider numerical methods for a singularly perturbed reaction-diffusion problem with a discontinuous source term. We show that such a problem arises naturally in the context of models of simple semiconductor devices. We construct a numerical method consisting of a standard finite difference operator and a non-standard piecewise-uniform mesh. The mesh is fitted to the boundary and interior layers that occur in the solution of the problem. We show by extensive computations that, for this problem, this method is parameter-uniform in the maximum norm, in the sense that the numerical solutions converge in the maximum norm uniformly with respect to the singular perturbation parameter, (C) 2000 IMACS. Published by Elsevier Science B.V. All rights reserved.
AB - In this paper we consider numerical methods for a singularly perturbed reaction-diffusion problem with a discontinuous source term. We show that such a problem arises naturally in the context of models of simple semiconductor devices. We construct a numerical method consisting of a standard finite difference operator and a non-standard piecewise-uniform mesh. The mesh is fitted to the boundary and interior layers that occur in the solution of the problem. We show by extensive computations that, for this problem, this method is parameter-uniform in the maximum norm, in the sense that the numerical solutions converge in the maximum norm uniformly with respect to the singular perturbation parameter, (C) 2000 IMACS. Published by Elsevier Science B.V. All rights reserved.
U2 - 10.1016/S0168-9274(99)00140-3
DO - 10.1016/S0168-9274(99)00140-3
M3 - Article
SN - 0168-9274
VL - 35
SP - 323
EP - 337
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
IS - 4
ER -