Convergence Rates of Domain Decomposition Methods for a Singularly Perturbed Convection-Diffusion Problem
by
Vic Duoba
Institute of Fundamental Sciences, Mathematics, Massey University, Palmerston North
Coauthors: Igor Boglaev (Institute of Fundamental Sciences, Mathematics, Massey University, Palmerston North)

Singularly perturbed partial differential equations commonly arise in convection-diffusion problems and are characterised by the presence of a small, positive multiplier of the high order term(s) of partial differential operators. Numerical solutions should ideally resolve any boundary layers, be stable and be computationally tractable in terms of the total computing effort. This paper examines the use of classical finite difference upwind methods using special meshes from a domain decomposition perspective. Results of numerical validation of some theoretical estimates on covergence rates are presented.

Date received: September 26, 2000