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A New Convergence Proof for the Multigrid Method Including the V -Cycle
D. Braess, W. Hackbusch
Source abstract
For a positive definite finite element equation we describe a multigrid iteration and prove convergence under natural assumptions on the discretization and the elliptic problem. Hitherto existing convergence proofs require a sufficiently large number of smoothing iterations and exclude the “V-cycle”. The presented proof applies to procedures with any number of smoothing iterations and to the V-cycle.
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