Convergence of nonconforming multigrid methods without full elliptic regularity

Brenner, Susanne

doi:10.1090/S0025-5718-99-01035-2

Convergence of nonconforming multigrid methods without full elliptic regularity
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Math. Comp. 68 (1999), 25-53 Request permission

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 ($<1$) for the contraction number of the $W$-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 $V$-cycle algorithm is an optimal preconditioner.

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