An operator Newton method for the Stefan problem based on smoothing: A local perspective
type: Item
instance of: scholarly article
title: An operator Newton method for the Stefan problem based on smoothing: A local perspective
zbMATH Open document ID: 0727.35143
DOI: 10.1016/0021-9045(90)90053-S
author: Joseph W. Jerome
published in: Journal of Approximation Theory
publication date: 1990-01-01T00:00:00Z
review text: The enthalpy formulation for the two-phase Stefan problem leads to the equation \(\partial H(u)/\partial t-\Delta u=0\), where H is discontinuous. For numerical purposes, H is often replaced by a smooth function \(H_{\epsilon}\). The author studies the convergence to the true solution u of the solutions \(u_{\epsilon}\) of the problems \(\partial H_{\epsilon}(u_{\epsilon})/\partial t-\Delta u_{\epsilon}=R_{\epsilon}\), where \(R_{\epsilon}\) is a residual that accounts for errors in the solution of the regularized problem. The solution of the regularized equations by Newton method is also investigated.
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35A35
zbMATH DE Number: 4200824
zbMATH Keywords: two-phase Stefan problem
zbMATH Keywords: convergence
zbMATH Keywords: regularized equations
zbMATH Keywords: Newton method
reviewed by: Jesús María Sanz-Serna
MaRDI profile type: Publication
cites work: Error Analysis of the Enthalpy Method for the Stefan Problem
cites work: Approximation of nonlinear evolution systems
cites work: Approximate Newton methods and homotopy for stationary operator equations
cites work: Error Estimates for the Multidimensional Two-Phase Stefan Problem
cites work: Energy error estimates for a linear scheme to approximate nonlinear parabolic problems
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description: scientific article; zbMATH DE number 4200824