The asymptotic behavior of multigrid V-cycle and F-cycle algorithms for the biharmonic problem using the Morley element are presented in this talk. By the use of an additive theory, we show that the contraction numbers of the algorithms can be uniformly improved as the number of smoothing steps increases, without assuming full elliptic regularity.

We describe the critical estimates required for the additive theory. Experimental results are also presented for the algorithms on convex and nonconvex domains. The results are consistent with the theoretical estimates.