Convergence of de Boor's algorithm for the generation of equidistributing meshes.

A commonly used algorithm for generating adaptive meshes for a given adaptation function in one dimension is due to de Boor. In its original form the algorithm produces a sequence of meshes upon using piecewise constant interpolation for the adaptation function on the current mesh and generating a new mesh that exactly equidistributes the interpolant. In this paper we present a proof for the existence of a limit mesh and for the convergence of de Boor's algorithm. Numerical results are given to illustrate the theoretical findings, and stopping criteria necessary for the implementation of the algorithm are examined. [ABSTRACT FROM PUBLISHER]