A simpler analysis of a hybrid numerical method for time-dependent convection-diffusion problems |
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Authors: | C Clavero JL Gracia |
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Institution: | a Department of Applied Mathematics, University of Zaragoza, Spainb Department of Mathematics, National University of Ireland, Cork, Ireland |
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Abstract: | A finite difference method for a time-dependent convection-diffusion problem in one space dimension is constructed using a Shishkin mesh. In two recent papers (Clavero et al. (2005) 2] and Mukherjee and Natesan (2009) 3]), this method has been shown to be convergent, uniformly in the small diffusion parameter, using somewhat elaborate analytical techniques and under a certain mesh restriction. In the present paper, a much simpler argument is used to prove a higher order of convergence (uniformly in the diffusion parameter) than in 2] and 3] and under a slightly less restrictive condition on the mesh. |
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Keywords: | Convection-diffusion parabolic problem Uniform convergence Shishkin mesh Hybrid finite difference scheme |
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