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On the stabilization of tetrahedral finite elements using volume and area bubble functions
Author(s) -
Caylak Ismail,
Mahnken Rolf
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700224
Subject(s) - tetrahedron , bubble , finite element method , nonlinear system , discontinuous galerkin method , mathematics , finite volume method , volume (thermodynamics) , current (fluid) , galerkin method , interpretation (philosophy) , mathematical analysis , physics , geometry , mechanics , thermodynamics , computer science , quantum mechanics , programming language
In order to overcome the oscillatory effects of the bi‐linear Galerkin formulation for tetrahedral elements the mixed method of incompatible modes and the mixed method of enhanced strains are reformulated, thus giving both the interpretation of a mixed finite element method with stabilization terms. For nonlinear problems these are nonlinearly dependent on the current deformation state, and therefore are replaced by linearly dependent stabilization terms. The approach becomes most attractive for the numerical implementation, since the use of quantities related to the previous Newton iteration step, typically arising for mixed enhanced elements, is completely avoided. The stabilization matrices for the mixed method of incompatible modes and the mixed method of enhanced strains are obtained with volume and area bubble functions. Cook's membrane problem illustrates successfully the stabilization effect for bi‐linear tetrahedral elements. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)