On the Robustness of Two-Level Preconditioners for Quadratic FE Orthotropic Elliptic Problems

  • J. Kraus
  • M. Lymbery
  • S. Margenov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7116)


We study the construction of subspaces for quadratic FEM orthotropic elliptic problems with a focus on the robustness with respect to mesh and coefficient anisotropy. In the general setting of an arbitrary elliptic operator it is known that standard hierarchical basis (HB) techniques do not result in splittings in which the angle between the coarse space and its (hierarchical) complement is uniformly bounded with respect to the ratio of anisotropy. In this paper we present a robust splitting of the finite element space of continuous piecewise quadratic functions for the orthotropic problem. As a consequence of this result we obtain also a uniform condition number bound for a special sparse Schur complement approximation. Further we construct a uniform preconditioner for the pivot block with optimal order of computational complexity.


Anisotropy Ratio Coarse Space Hierarchical Basis Spectral Condition Number Relative Condition Number 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • J. Kraus
    • 1
  • M. Lymbery
    • 2
  • S. Margenov
    • 2
  1. 1.Johann Radon Institute for Computational and Applied MathematicsAustrian Academy of SciencesLinzAustria
  2. 2.Institute of Information and Communication TechnologiesBulgarian Academy of SciencesSofiaBulgaria

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