An algorithm for coarsening unstructured meshes

Randolph E. Bank, Jinchao Xu

Research output: Contribution to journalArticle

66 Scopus citations

Abstract

We develop and analyze a procedure for creating a hierarchical basis of continuous piecewise linear polynomials on an arbitrary, unstructured, nonuniform triangular mesh. Using these hierarchical basis functions, we are able to define and analyze corresponding iterative methods for solving the linear systems arising from finite element discretizations of elliptic partial differential equations. We show that such iterative methods perform as well as those developed for the usual case of structured, locally refined meshes. In particular, we show that the generalized condition numbers for such iterative methods are of order J2, where J is the number of hierarchical basis levels.

Original languageEnglish (US)
Pages (from-to)1-36
Number of pages36
JournalNumerische Mathematik
Volume73
Issue number1
DOIs
StatePublished - Mar 1996

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

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