A polylogarithmic bound for an iterative substructuring method for spectral elements in three dimensions

Luca F. Pavarino, Olof B. Widlund

Research output: Contribution to journalArticle

Abstract

Iterative substructuring methods form an important family of domain decomposition algorithms for elliptic finite element problems. A p-version finite element method based on continuous, piecewise Qp functions is considered for second-order elliptic problems in three dimensions; this special method can also be viewed as a conforming spectral element method. An iterative method is designed for which the condition number of the relevant operator grows only in proportion to ( 1 + log p)2. This bound is independent of jumps in the coefficient of the elliptic problem across the interfaces between the subregions. Numerical results are also reported which support the theory.

Original languageEnglish (US)
Pages (from-to)1303-1335
Number of pages33
JournalSIAM Journal on Numerical Analysis
Volume33
Issue number4
DOIs
StatePublished - Aug 1996

Keywords

  • Domain decomposition
  • Iterative substructuring
  • Spectral approximation
  • p-version finite elements

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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