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Numerical simulation of (nearly) incompressible material, using adaptive mixed finite element method
Author(s) -
Balg Martina,
Meyer Arnd
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110370
Subject(s) - finite element method , saddle point , compressibility , conjugate gradient method , mixed finite element method , extended finite element method , nonlinear system , mathematics , hydrostatic equilibrium , convergence (economics) , mathematical analysis , mathematical optimization , mechanics , physics , geometry , quantum mechanics , economics , thermodynamics , economic growth
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)