Combined effect of explicit time-stepping and quadrature for curvature driven flows
type: Item
instance of: scholarly article
title: Combined effect of explicit time-stepping and quadrature for curvature driven flows
zbMATH Open document ID: 0859.65066
author: Ricardo H. Nochetto
author: Claudio Verdi
published in: Numerische Mathematik
publication date: 1997-03-25T00:00:00Z
review text: The flow of a closed surface of codimension 1 in \(\mathbb{R}^n\) driven by curvature is first approximated by a singularly perturbed parabolic double obstacle problem with small parameter. The discretization is made by conforming piecewise linear finite elements, with mass lumping, over a quasi-uniform and weakly acute mesh combined with forward differences with uniform time-step. An efficient algorithm, the so-called dynamic mesh algorithm, is obtained. It shows finite speed of propagation and discrete nondegeneracy. It is demonstrated that the fully discrete solution converges past singularities to the true interface and the rate of convergence is discussed. Smooth flows are also analyzed.
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 49Q05
Mathematics Subject Classification ID: 49M15
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 35B50
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 932011
zbMATH Keywords: explicit time-stepping
zbMATH Keywords: quadrature
zbMATH Keywords: curvature driven flows
zbMATH Keywords: double obstacle problem
zbMATH Keywords: linear finite elements
zbMATH Keywords: dynamic mesh algorithm
zbMATH Keywords: convergence
reviewed by: Viorel Arnăutu
MaRDI profile type: Publication
full work available at URL: s002110050210
OpenAlex ID: W2090075180
DOI: 10.1007/S002110050210
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description: scientific article; zbMATH DE number 932011