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A Subspace Correction Method for Nearly Singular Linear Elasticity Problems

  • E. KarerEmail author
  • J. K. Kraus
  • L. T. Zikatanov
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 91)

Abstract

The focus of this work is on constructing a robust (uniform in the problem parameters) iterative solution method for the system of linear algebraic equations arising from a nonconforming finite element discretization based on reduced integration.We introduce a specific space decomposition into two overlapping subspaces that serves as a basis for devising a uniformly convergent subspace correction algorithm. We consider the equations of linear elasticity in primal variables. For nearly incompressible materials, i.e., when the Poisson ratio \(\nu\;\mathrm{approaches}\;1/2 \), this problem becomes ill-posed and the resulting discrete problem is nearly singular.

Keywords

Multigrid Method Space Decomposition Auxiliary Space Linear Elasticity Problem Iterative Solution Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

Acknowledgements

The authors gratefully acknowledge the support by the Austrian Academy of Sciences and by the Austrian Science Fund (FWF), Project No. P19170-N18 and by the National Science Foundation NSF-DMS 0810982.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Johann Radon Institute for Computational and Applied MathematicsAustrian Academy of SciencesLinzAustria
  2. 2.Penn State University, State CollegeUniversity ParkUSA

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