Convergence of a finite element method for non-parametric mean curvature flow
type: Item
instance of: scholarly article
title: Convergence of a finite element method for non-parametric mean curvature flow
zbMATH Open document ID: 0838.65103
published in: Numerische Mathematik
publication date: 1996-06-03T00:00:00Z
review text: This paper is devoted to a finite element method for the mean curvature flow equation, a convection-diffusion equation in which the convection depends on the mean curvature of the level surfaces. Dirichlet problems are considered on a bounded domain \(\Omega\) in the plane. For the finite element method \(\Omega\) is divided into triangles, for which a side on \(\partial \Omega\) may be curved. The basis functions are linear on each triangle. Convergence proofs and error estimates are given. The proofs are based on a homotopy from the parabolic minimal-surface equation.
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 839155
zbMATH Keywords: convergence
zbMATH Keywords: finite element method
zbMATH Keywords: mean curvature flow equation
zbMATH Keywords: convection-diffusion equation
zbMATH Keywords: Dirichlet problems
zbMATH Keywords: error estimates
zbMATH Keywords: parabolic minimal-surface equation
author: Klaus Deckelnick
author: G. Dziuk
reviewed by: Gerald W. Hedstrom
MaRDI profile type: Publication
full work available at URL: s002110050166
OpenAlex ID: W1965110070
DOI: 10.1007/S002110050166
description: scientific article; zbMATH DE number 839155