Error estimates for two-phase Stefan problems in several space variables. I: Linear boundary conditions
type: Item
instance of: scholarly article
title: Error estimates for two-phase Stefan problems in several space variables. I: Linear boundary conditions
zbMATH Open document ID: 0606.65084
DOI: 10.1007/BF02575898
published in: Calcolo
publication date: 1985-01-01T00:00:00Z
review text: The enthalpy formulation of two-phase Stefan problems, with linear boundary conditions, is approximated by \(C^ 0\)-piecewise linear finite elements in space and backward-differences in time combined with a regularization procedure. Error estimates of \(L^ 2\)-type are obtained. For general regularized problems an order \(\epsilon^{1/2}\) is proved, while the order is shown to be \(\epsilon\) for non-degenerate cases. For discrete problems an order \(h^ 2\epsilon^{-1}+h+\tau \epsilon^{- }+\tau^{2/3}\) is obtained. These orders impose the relations \(\epsilon \sim \tau \sim h^{4/3}\) for the general case and \(\epsilon \sim h\sim \tau^{2/3}\) for non-degenerate problems, in order to obtain rates of convergence \(h^{2/3}\) or h respectively. Besides, an order \(h| \log h| +\tau^{1/2}\) is shown for finite element meshes with certain approximation property. Also continuous dependence of discrete solutions upon the data is proved.
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 80A17
Mathematics Subject Classification ID: 35R35
zbMATH DE Number: 3980429
zbMATH Keywords: two-phase Stefan problems
zbMATH Keywords: linear finite elements in space
zbMATH Keywords: backward- differences in time
zbMATH Keywords: regularization
zbMATH Keywords: Error estimates
zbMATH Keywords: rates of convergence
author: Ricardo H. Nochetto
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02575898
OpenAlex ID: W2083229688
description: scientific article; zbMATH DE number 3980429