Multigrid convergence for a singular perturbation problem
The behaviour of multigrid methods applied to singularly perturbed elliptic boundary value problems is analysed for the one-dimensional model problem \(-\epsilon u''+u'=f\) with periodic and Dirichlet boundary conditions. A close relationship between these cases is established. This allows to apply the results of a Fourier analysis for periodic boundary conditions to the case of Dirichlet boundary conditions. It should be noted that the Fourier analysis is not directly applicable to the latter case.
scientific article; zbMATH DE number 3868539
scientific article