Numerical simulation of (nearly) incompressible material, using adaptive mixed finite element method

In this paper we present a way to numerically simulate large deformations of incompressible material and the corresponding hydrostatic pressure by using a mixed, adaptive finite element method (FEM). Starting from the system of differential equations we will derive the weak nonlinear formulation, which can be solved with a Newton's method. In every iteration step this will lead to a saddle point problem. By using Taylor Hood finite elements we will obtain a discrete, indefinite problem, which can be handled with the Bramble Pasciak conjugate gradient method. Finally we give a numerical example. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)