A V-cycle multigrid method and additive multilevel preconditioners for the plate bending problem discretized by conforming finite elements

Abstract

It is well known that many conforming plate finite element spaces in the multilevel methods are nonnested even when the triangulations are nested, so it is difficult to construct the effective V-cycle multigrid method and multilevel preconditioners for the plate bending problem. In this paper, a new method dealing with multilevel methods for finite element discretisation equations of the plate problem is developed. An optimal V-cycle multigrid method and multilevel preconditioners for some famous conforming plate elements are constructed. Moreover, our methods can be applied to the plate problem with complicated geometries.