Monotone Schwarz iterates for a semilinear parabolic convection–diffusion problem

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摘要

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.

论文关键词:Singular perturbation,Convection–diffusion problem,Monotone Schwarz algorithm,Uniform convergence

论文评审过程:Received 4 May 2004, Revised 20 January 2005, Available online 3 March 2005.

论文官网地址:https://doi.org/10.1016/j.cam.2005.01.012