Approximation of a second order Stefan-like problem by means of a finite element method
type: Item
instance of: scholarly article
title: Approximation of a second order Stefan-like problem by means of a finite element method
zbMATH Open document ID: 0556.65095
DOI: 10.1007/BF02576467
published in: Calcolo
publication date: 1983-01-01T00:00:00Z
review text: For the equation \(U_{yy}-U_{\tau}=0\) a Stefan-like problem is treated in which the time derivative of the free boundary depends on its position, on time, on U and on \(U_{yy}\) (the latter two taken at the position of the free boundary). The problem is transformed into one with fixed boundary, and then existence and uniqueness are established (under appropriate assumptions and after introduction of suitable function spaces) by a further transformation into a fixed point equation with contractive operator. The iteration operator is approximated by finite element discretization of the space variable, convergence for refinement of the grid is shown, and an error estimate is given. Finally the author demonstrates the applicability of his method by displaying results of a numerical case study (in which, of course, the time variable too is discretized).
reviewed by: Rudolf Gorenflo
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 80A17
zbMATH DE Number: 3887053
zbMATH Keywords: finite elements
zbMATH Keywords: Stefan problem
zbMATH Keywords: numerical example
zbMATH Keywords: fixed point
zbMATH Keywords: contractive operator
zbMATH Keywords: iteration operator
zbMATH Keywords: convergence
zbMATH Keywords: refinement
zbMATH Keywords: error estimate
author: Lucia Gastaldi
MaRDI profile type: Publication
cites work: Q4162607
cites work: Free boundary problems for nonlinear parabolic equations with nonlinear free boundary conditions
cites work: General free-boundary problems for the heat equation. I
cites work: Q5520962
cites work: Q3907030
cites work: Q3921604
cites work: On the multivalence of a class of meromorphic functions
description: scientific article; zbMATH DE number 3887053