Application of Hierarchical Decomposition: Preconditioners and Error Estimates for Conforming and Nonconforming FEM

  • Radim Blaheta
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4818)


A successive refinement of a finite element grid provides a sequence of nested grids and hierarchy of nested finite element spaces as well as a natural hierarchical decomposition of these spaces. In the case of numerical solution of elliptic boundary value problems by the conforming FEM, this sequence can be used for building both multilevel preconditioners and error estimates. For a nonconforming FEM, multilevel preconditioners and error estimates can be introduced by means of a hierarchy, which is constructed algebraically starting from the finest discretization.


Hierarchical Decomposition Nest Grid Numerical Linear Algebra Hierarchical Basis Nonconforming Finite Element 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Radim Blaheta
    • 1
  1. 1.Department of Applied MathematicsInstitute of Geonics AS CROstrava-PorubaCzech Republic

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