Convergence of the multigrid 𝑉-cycle algorithm for second-order boundary value problems without full elliptic regularity

Brenner, Susanne

doi:10.1090/S0025-5718-01-01361-8

Convergence of the multigrid $V$-cycle algorithm for second-order boundary value problems without full elliptic regularity
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Math. Comp. 71 (2002), 507-525 Request permission

Abstract:

The multigrid $V$-cycle algorithm using the Richardson relaxation scheme as the smoother is studied in this paper. For second-order elliptic boundary value problems, the contraction number of the $V$-cycle algorithm is shown to improve uniformly with the increase of the number of smoothing steps, without assuming full elliptic regularity. As a consequence, the $V$-cycle convergence result of Braess and Hackbusch is generalized to problems without full elliptic regularity.

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