Convergence of the multigrid V-cycle algorithm for second-order boundary value problems without full elliptic regularity
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.
Publication Source (Journal or Book title)
Mathematics of Computation
Brenner, S. (2002). Convergence of the multigrid V-cycle algorithm for second-order boundary value problems without full elliptic regularity. Mathematics of Computation, 71 (238), 507-525. https://doi.org/10.1090/S0025-5718-01-01361-8