Computational Mechanics

, Volume 54, Issue 2, pp 523–533 | Cite as

A stabilization technique for the regularization of nearly singular extended finite elements

  • Stefan LoehnertEmail author
Original Paper


In this contribution a simple, robust and efficient stabilization technique for extended finite element (XFEM) simulations is presented. It is useful for arbitrary crack geometries in two or three dimensions that may lead to very bad condition numbers of the global stiffness matrix or even ill-conditioning of the equation system. The method is based on an eigenvalue decomposition of the element stiffness matrix of elements that only possess enriched nodes. Physically meaningful zero eigenmodes as well as enrichment scheme dependent numerically reasonable zero eigenmodes are filtered out. The remaining subspace is stabilized depending on the magnitude of the respective eigenvalues. One of the main advantages is the fact that neither the equation solvers need to be changed nor the solution method is restricted. The efficiency and robustness of the method is demonstrated in numerous examples for 2D and 3D fracture mechanics.


XFEM Stabilization Cracks Conditioning 



The support of the German Research Foundation (DFG) within the framework of the grant SFB 871 is gratefully acknowledged.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Institute of Continuum MechanicsHannoverGermany

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