Robust Block Preconditioners for Biot’s Model

  • James H. AdlerEmail author
  • Francisco J. GasparEmail author
  • Xiaozhe HuEmail author
  • Carmen RodrigoEmail author
  • Ludmil T. ZikatanovEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 125)


In this paper, we design robust and efficient block preconditioners for the two-field formulation of Biot’s consolidation model, where stabilized finite-element discretizations are used. The proposed block preconditioners are based on the well-posedness of the discrete linear systems. Block diagonal (norm-equivalent) and block triangular preconditioners are developed, and we prove that these methods are robust with respect to both physical and discretization parameters. Numerical results are presented to support the theoretical results.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsTufts UniversityMedfordUSA
  2. 2.Departamento de Matemática AplicadaUniversidad de ZaragozaZaragozaSpain
  3. 3.Department of MathematicsPenn StateUniversity ParkUSA

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