Numerische Mathematik

, Volume 73, Issue 1, pp 1-36

First online:

An algorithm for coarsening unstructured meshes

  • Randolph E. BankAffiliated withDepartment of Mathematics, University of California at San Diego, La Jolla, CA 92093, USA
  • , Jinchao XuAffiliated withDepartment of Mathematics, Penn State University, University Park, PA 16802, USA

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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