Abstract
Various variants of Schwarz methods for a singularly perturbed two dimensional stationary convection-diffusion problem are constructed and analysed. The iteration counts, the errors in the discrete solutions and the convergence behaviour of the numerical solutions are analysed in terms of their dependence on the singular perturbation parameter of the Schwarz methods. Conditions for the methods to converge parameter uniformly and for the number of iterations to be independent of the perturbation parameter are discussed.
This research was supported in part by the DCU Research Grant RC98-SPRJ- 12EOR, by the Enterprise Ireland grant SC-98-612 and by the Russian Foundation for Basic Research under grant No. 98-01-00362.
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MacMullen, H., OĊiordan, E., Shishkin, G.I. (2001). Schwarz Methods for Convection-Diffusion Problems. In: Vulkov, L., Yalamov, P., WaĊniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2000. Lecture Notes in Computer Science, vol 1988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45262-1_64
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DOI: https://doi.org/10.1007/3-540-45262-1_64
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