An operator Newton method for the Stefan problem based on smoothing: A local perspective

Joseph W. Jerome*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The initial/Neumann boundary-value enthalpy formulation for the two-phase Stefan problem is regularized by smoothing. Known estimates predict a convergence rate of ε 1 2, and this result is extended in this paper to include the case of a (nonzero) residual in the regularized problem. A modified Newton Kantorovich framework is established, whereby the exact solution of the regularized problem is replaced by one Newton iteration. It is shown that a consistent theory requires measure-theoretic hypotheses on the starting guess and the Newton iterate, otherwise residual decrease is not expected. The circle closes in one spatial dimension, where it is shown that the residual decrease of Newton's method correlates precisely with the ε 1 2 convergence theory.

Original languageEnglish (US)
Pages (from-to)282-296
Number of pages15
JournalJournal of Approximation Theory
Volume62
Issue number3
DOIs
StatePublished - Sep 1990

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Mathematics(all)
  • Applied Mathematics

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