Numerische Mathematik

, Volume 132, Issue 1, pp 23–49 | Cite as

A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations

  • Qingguo Hong
  • Johannes KrausEmail author
  • Jinchao Xu
  • Ludmil Zikatanov


We consider multigrid methods for discontinuous Galerkin \(H({\text {div}},\Omega )\)-conforming discretizations of the Stokes and linear elasticity equations. We analyze variable V-cycle and W-cycle multigrid methods with nonnested bilinear forms. We prove that these algorithms are optimal and robust, i.e., their convergence rates are independent of the mesh size and also of the material parameters such as the Poisson ratio. Numerical experiments are conducted that further confirm the theoretical results.

Mathematics Subject Classification

65N55 65N30 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Qingguo Hong
    • 1
  • Johannes Kraus
    • 2
    Email author
  • Jinchao Xu
    • 3
  • Ludmil Zikatanov
    • 3
    • 4
  1. 1.Johann Radon InstituteAustrian Academy of SciencesLinzAustria
  2. 2.Faculty of MathematicsUniversity of Duisburg-EssenEssenGermany
  3. 3.Department of MathematicsPennsylvania State UniversityUniversity ParkUSA
  4. 4.Institute of Mathematics and InformaticsBulgarian Academy of SciencesSofiaBulgaria

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