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

被引:22
作者
Clavero, C. [1 ]
Gracia, J. L. [1 ]
Stynes, M. [2 ]
机构
[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; MESHES;
D O I
10.1016/j.cam.2011.05.025
中图分类号
O29 [应用数学];
学科分类号
070104 ;
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.
引用
收藏
页码:5240 / 5248
页数:9
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