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

Authors:
Radim Blaheta
Affiliations:
Department of Applied Mathematics, Institute of Geonics AS CR, Ostrava-Poruba, Czech Republic 70800
Venue:
Large-Scale Scientific Computing
Year:
2009

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Abstract

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.