Numerische Mathematik

, Volume 73, Issue 1, pp 1–36 | Cite as

An algorithm for coarsening unstructured meshes

  • Randolph E. Bank
  • Jinchao Xu


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 \(J^2\), where \(J\) is the number of hierarchical basis levels.

Mathematics Subject Classification (1991):65F10, 65N20 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Randolph E. Bank
    • 1
  • Jinchao Xu
    • 2
  1. 1.Department of Mathematics, University of California at San Diego, La Jolla, CA 92093, USA US
  2. 2.Department of Mathematics, Penn State University, University Park, PA 16802, USA US

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