A simpler analysis of a hybrid numerical method for time-dependent convection-diffusion problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:235

Article

Clavero, C.¹  Gracia, J. L.¹  Stynes, M.² 

[1] Univ Zaragoza, Dept Appl Math, E-50009 Zaragoza, Spain

[2] Natl Univ Ireland, Dept Math, Cork, Ireland

关键词: Convection-diffusion parabolic problem;    Uniform convergence;    Shishkin mesh;    Hybrid finite difference scheme;   

DOI  :  10.1016/j.cam.2011.05.025

来源: Elsevier

【 摘 要 】

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 [2,3] and under a slightly less restrictive condition on the mesh. (c) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

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