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Adaptive Solution Of Parabolic Free Boundary Problems With Error Control

By R.H. Nochetto, A. Schmidt and C. Verdi

Abstract

We derive a posteriori error estimates in natural energy norms with weights. They are useful in localizing the error extraction in regions of interest, and form the basis of an adaptive procedure. We use them to study the evolution of a persistent corner singularity and elucidate the issue of critical angle for instantaneous smoothing. 1 Introduction The presence of interfaces, and associated lack of regularity, is responsible for global numerical pollution effects for parabolic free boundary problems. A cure consists of equidistributing discretization errors in adequate norms by means of highly graded meshes and varying time steps. Their construction relies on a posteriori error estimates, which are a fundamental component for the design of reliable and efficient adaptive algorithms for PDEs. These issues have been recently tackled in [6], [7], [8], [9], and are briefly discussed here. We consider for simplicity the classical two-phase Stefan problem for an ideal material with consta..

Year: 2007
OAI identifier: oai:CiteSeerX.psu:10.1.1.36.9928
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