An \(H^ 1\)-Galerkin method for a Stefan problem with a quasilinear parabolic equation in nondivergence form
type: Item
instance of: scholarly article
title: An \(H^ 1\)-Galerkin method for a Stefan problem with a quasilinear parabolic equation in nondivergence form
zbMATH Open document ID: 0622.65125
DOI: 10.1155/S0161171287000413
author: B. George
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46196
review text: A one-dimensional single-phase Stefan problem is studied both from the theoretical and numerical view point. The problem is first transformed into a quasilinear parabolic equation which is not in divergence form. This parabolic problem is studied through a variational (weak) formulation. Approximation by an \(H^ 1\)-Galerkin procedure is then discussed and optimal error estimates in \(L^ 2\), \(H^ 1\), \(H^ 2\) norms are obtained.
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 80A17
Mathematics Subject Classification ID: 35R35
zbMATH DE Number: 4009751
zbMATH Keywords: Galerkin method
zbMATH Keywords: finite elements
zbMATH Keywords: nondivergence form
zbMATH Keywords: single-phase Stefan problem
zbMATH Keywords: quasilinear parabolic equation
zbMATH Keywords: optimal error estimates
MaRDI profile type: Publication
OpenAlex ID: W2120689572
description: scientific article; zbMATH DE number 4009751