Local and parallel finite element algorithms based on two-grid discretizations

Jinchao Xu, Aihui Zhou

Research output: Contribution to journalArticlepeer-review

151 Scopus citations

Abstract

A number of new local and parallel discretization and adaptive finite element algorithms are proposed and analyzed in this paper for elliptic boundary value problems. These algorithms are motivated by the observation that, for a solution to some elliptic problems, low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on a fine grid by some local and parallel procedure. The theoretical tools for analyzing these methods are some local a priori and a posteriori estimates that are also obtained in this paper for finite element solutions on general shape-regular grids. Some numerical experiments are also presented to support the theory.

Original languageEnglish (US)
Pages (from-to)881-909
Number of pages29
JournalMathematics of Computation
Volume69
Issue number231
DOIs
StatePublished - Jul 2000

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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