Monotone Schwarz iterates for a semilinear parabolic convection-diffusion problem

Authors:
Igor Boglaev
Affiliations:
Institute of Fundamental Sciences, Massey University, Private Bag 11-222, Palmerston North, New Zealand
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

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Abstract

This paper deals with a discrete monotone iterative algorithm for solving a nonlinear singularly perturbed convection-diffusion problem of parabolic type. On each time level, the monotone method (known as the method of lower and upper solutions) is applied to computing a nonlinear upwind difference scheme obtained after discretisation of the continuous problem. A monotone domain decomposition algorithm based on a modification of the Schwarz alternating method is constructed. The rate of convergence of the monotone Schwarz method is estimated. Uniform convergence properties of the monotone domain decomposition algorithm are studied. Numerical experiments are presented.