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

作者：Clavero C^*; Gracia J L; Stynes M

来源：Journal of Computational and Applied Mathematics, 2011, 235(17): 5240-5248.

DOI：10.1016/j.cam.2011.05.025

• Convection-diffusion parabolic problem
• Uniform convergence
• Shishkin mesh
• Hybrid finite difference scheme

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.

• 出版日期2011-7-1