Summary
The multilevel Full Approximation Scheme (FAS ML) is a well-known solver for nonlinear boundary value problems. In this paper we prove local quantitative convergence statements for a class of FAS ML algorithms in a general Hilbertspace setting. This setting clearly exhibits the structure of FAS ML. We prove local convergence of a nested iteration for a rather concrete class of FAS ML algorithms in whichV-cycles and only one Jacobilike pre- and post-smoothing on each level are used.
This is a preview of subscription content, log in via an institution to check access.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
Allgower, E.L., Böhmer, K., Potra, F.A., Rheinboldt, W.C.: A mesh-independence principle for operator equations and their discretizations. SIAM J. Numer. Anal.23, 160–169 (1986)
Bank, R.E., Douglas, C.C.: Sharp estimates for multigrid rates of convergence with general smoothing and acceleration. SIAM J. Numer. Anal.22, 617–633 (1985)
Bank, R.E., Rose, D.J.: Analysis of a multilevel iterative method for nonlinear finite element equations. Math. Comput.39, 453–465 (1982)
Braess, D., Hackbusch, W.: A new convergence proof for the multigrid method including theV-cycle. SIAM J. Numer. Anal.20, 967–975 (1983)
Hackbusch, W.: Multigrid methods and applications. Berlin Heidelberg New York Tokyo: Springer 1985
Reusken, A.: Convergence of the multrigrid full approximation scheme for a class of elliptic mildly nonlinear boundary value problems. Numer. Math.52, 251–277 (1988)
Sion, M.: On general minimax theorems. Pac. J. Math.8, 171–176 (1958)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Reusken, A. Convergence of the multilevel Full Approximation Scheme including theV-cycle. Numer. Math. 53, 663–686 (1988). https://doi.org/10.1007/BF01397135
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01397135