Error estimates for a semi-implicit fully discrete element scheme for the mean curvature flow of graphs
type: Item
instance of: scholarly article
title: Error estimates for a semi-implicit fully discrete element scheme for the mean curvature flow of graphs
zbMATH Open document ID: 0974.65088
DOI: 10.4171/IFB/24
author: Klaus Deckelnick
author: G. Dziuk
published in: Interfaces and Free Boundaries
publication date: 2001-11-29T00:00:00Z
review text: The aim of this paper is to analyse a fully discrete finite element algorithm that approximates the mean curvature flow of graphs. The highly nonlinear problem is discretized in space by piecewise linear finite elements. The problem is written in a variational form which allows the use of the modern adaptive techniques of finite elements. The time discretization is carried out in a semi-implicit way such that in every time step a linear system with symmetric positive matrix has to be solved. Optimal error estimates are proved for the fully discrete problem under the assumption that the time-step size is bounded by the spatial grid size.
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35G25
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 1545559
zbMATH Keywords: numerical simulation
zbMATH Keywords: mean curvature flow of graphs
zbMATH Keywords: interface
zbMATH Keywords: finite elements
zbMATH Keywords: variational form
zbMATH Keywords: time discretization
zbMATH Keywords: optimal error estimates
reviewed by: Leonid B. Chubarov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1545559