Some numerical experiments with multigrid methods on Shishkin meshes
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摘要
Piecewise uniform meshes introduced by Shishkin, are a very useful tool to construct robust and efficient numerical methods to approximate the solution of singularly perturbed problems. For small values of the diffusion coefficient, the step size ratios, in this kind of grids, can be very large. In this case, standard multigrid methods are not convergent. To avoid this troublesome, in this paper we propose a modified multigrid algorithm, which works fine on Shishkin meshes. We show some numerical experiments confirming that the proposed multigrid method is convergent, and it has similar properties that standard multigrid for classical elliptic problems.
论文关键词:65N12,65N55,65N06,Singular perturbation,Shishkin mesh,Multigrid method
论文评审过程:Received 2 September 2000, Revised 11 January 2001, Available online 29 October 2001.
论文官网地址:https://doi.org/10.1016/S0377-0427(01)00365-X