Theoretical analysis of some spectral multigrid methods (Q1175229)

Multrigrid methods have previously been developed for spectral approximations of elliptic problems. In previous work by the author and \textit{Y. Maday} [J. Sci. Comput. 3, No. 4, 323-353 (1988; Zbl 0695.65058)] partial results were found for one-dimensional problems. In this paper, the two-level convergence rate is shown to be independent of the number of elements and the degree of the polynomials. A discussion is also given of two-dimensional problems. In that case, there are strong indications that these multigrid methods are not optimal.