Abstract
We consider nonconforming multigrid methods for symmetric positive definite second and fourth order elliptic boundary value problems which do not have full elliptic regularity. We prove that there is a bound ( > 1 >1 ) for the contraction number of the W W -cycle algorithm which is independent of mesh level, provided that the number of smoothing steps is sufficiently large. We also show that the symmetric variable V V -cycle algorithm is an optimal preconditioner.
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