On the inclusion principle for the hierarchical finite element method

L. Meirovitch, H. Baruh

Research output: Contribution to journalArticlepeer-review

50 Scopus citations


The inclusion principle provides a qualitative characterization of the eigenvalues of a matrix. The principle has been shown to apply to systems described by a single Hermitian matrix, the most important of which being the real symmetric matrix. Self‐adjoint distributed systems, when discretized by either the classical Rayleigh‐Ritz method or by the finite element method, lead to algebraic eigenvalue problems described in terms of two real symmetric matrices. The algebraic eigenvalues problem derived by the classical Rayleigh‐Ritz method possesses the embedding feature required by the inclusion principle, but that derived by the finite element method in general does not. This paper demonstrates that the inclusion principle can be extended to discretized systems derived by the hierarchical finite element method.

Original languageEnglish (US)
Pages (from-to)281-291
Number of pages11
JournalInternational Journal for Numerical Methods in Engineering
Issue number2
StatePublished - Feb 1983
Externally publishedYes

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics


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