Numerische Mathematik

, Volume 53, Issue 6, pp 663-686

First online:

Convergence of the multilevel Full Approximation Scheme including theV-cycle

  • Arnold ReuskenAffiliated withDepartment of Mathematics, University of Utrecht

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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.

Subject Classifications

AMS(MOS): 65N20 CR: G1.8