An algorithm for coarsening unstructured meshes

Randolph E. Bank, Jinchao Xu

Research output: Contribution to journalArticle

66 Citations (Scopus)

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 - Jan 1 1996

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Hierarchical Basis
Unstructured Mesh
Coarsening
Iterative methods
Iteration
Non-uniform Mesh
Triangular Mesh
Elliptic Partial Differential Equations
Finite Element Discretization
Condition number
Piecewise Linear
Partial differential equations
Linear systems
Basis Functions
Linear Systems
Polynomials
Mesh
Polynomial
Arbitrary

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

Cite this

Bank, Randolph E. ; Xu, Jinchao. / An algorithm for coarsening unstructured meshes. In: Numerische Mathematik. 1996 ; Vol. 73, No. 1. pp. 1-36.
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An algorithm for coarsening unstructured meshes. / Bank, Randolph E.; Xu, Jinchao.

In: Numerische Mathematik, Vol. 73, No. 1, 01.01.1996, p. 1-36.

Research output: Contribution to journalArticle

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