Monotone Multigrid Methods Based on Parametric Finite Elements

Abstract

In this paper, a particular technique for the application of elementary multilevel ideas to problems with warped boundaries is studied in the context of the numerical simulation of elastic contact problems. Combining a general multilevel setting with a different perspective, namely an advanced geometric modeling point of view, we present a (monotone) multigrid method based on a hierarchy of parametric finite element spaces. For the construction, a full-dimensional parameterization of high order is employed which accurately represents the computational domain.The purpose of the volume parametric finite element discretization put forward here is two-fold. On the one hand, it allows for an elegant multilevel hierarchy to be used in preconditioners. On the other hand, it comes with particular advantages for the modeling of contact problems. After all, the long-term objective lies in an increased flexibility of h p-adaptive methods for contact problems. © Springer-Verlag Berlin Heidelberg 2013.