Fourier analysis of a robust multigrid method for convection-diffusion equations
The author considers a two-dimensional convection-diffusion problem with constant coefficients and periodic boundary conditions. A particular two- grid method based on a finite difference approach and on an approximation of the Schur complement is presented. As a preconditioner the exact Schur complement of modified fine grid equations is used. By standard Fourier analysis numerous expressions for the eigenvalues of the Schur complement and of the preconditioner are proved. The main result consists in a theorem which establishes an upper bound for the spectral radius of the two-grid iteration matrix that is smaller than one and independent of the mesh size, the convection-diffusion ratio and the flow direction. Numerical results are also presented.
scientific article; zbMATH DE number 802475