Differentiability properties of solutions of the equation -ε2δ u + ru=f(x,y) in a square
SIAM Journal on Mathematical Analysis
Matrix-dependent prolongations and restrictions in a blackbox multigrid solver
Journal of Computational and Applied Mathematics
SIAM Journal on Scientific and Statistical Computing
Fourier analysis of a robust multigrid method for convection-diffusion equations
Numerische Mathematik
Fitted Numerical Methods for Singular Perturbation Problems: Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions
Multigrid Methods and Finite Difference Schemes for 2D Singularly Perturbed Problems
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Hi-index | 7.29 |
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.