On the Convergence of Iterated Remeshing

In the context of constructing a one-dimensional space-meshby equidistributing a weight function (monitor function) asintroduced by de Boor, we prove that under not too unrealistican approximation to the process as carried out in practice,iterating the remeshing process gives a convergent sequenceof meshes. The limit mesh has useful asymptotic smoothness properties.We suggest ways in which this could be exploited for improvederror control in BVPs. Numerical experiments show the convergencebehaviour, and give preliminary support to the error-controlproposal.