, Volume 64, Issue 4, pp 289–306 | Cite as

Robust Multigrid Methods for Nearly Incompressible Elasticity

  • Christian Wieners


We consider multigrid methods for problems in linear elasticity which are robust with respect to the Poisson ratio. Therefore, we consider mixed approximations involving the displacement vector and the pressure, where the pressure is approximated by discontinuous functions. Then, the pressure can be eliminated by static condensation. The method is based on a saddle point smoother which was introduced for the Stokes problem and which is transferred to the elasticity system. The performance and the robustness of the multigrid method are demonstrated on several examples with different discretizations in 2D and 3D. Furthermore, we compare the multigrid method for the saddle point formulation and for the condensed positive definite system.

AMS Subject Classifications: 65N55, 65N30. 
Key Words: Elasticity, robust multigrid methods. 


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Copyright information

© Springer-Verlag Wien 2000

Authors and Affiliations

  • Christian Wieners
    • 1
  1. 1.Interdisziplinäres Zentrum für wissenschaftliches Lernen Universität Heidelberg Im Neuenheimer Feld 368 D-69120 Heidelberg Germany e-mail: Christian.Wieners@iwr.uni-heidelberg.deDE

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