On the parametric finite element approximation of evolving hypersurfaces in R3

被引：123

作者：

Barrett, John W. ^{[1
]}

Garcke, Harald ^{[2
]}

Nurnberg, Robert ^{[1
]}

机构：

[1] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

[2] Univ Regensburg, NWF Math 1, D-93040 Regensburg, Germany

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2008年 / 227卷 / 09期

关键词：

surface diffusion; (inverse) mean curvature flow; surface attachment limited kinetics; nonlinear surface evolution; parametric finite elements; tangential movement;

D O I：

10.1016/j.jcp.2007.11.023

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We present a variational formulation of motion by minus the Laplacian of curvature and mean curvature flow, as well as related second and fourth order flows of a closed hypersurface in R-3. On introducing a parametric finite element approximation, we prove stability bounds and compare our scheme with existing approaches. The presented scheme has very good properties with respect to the distribution of mesh points and, if applicable, volume conservation. (C) 2007 Elsevier Inc. All rights reserved.

引用

页码：4281 / 4307

页数：27

共 31 条

[1] AXIOMS AND FUNDAMENTAL EQUATIONS OF IMAGE-PROCESSING [J].

ALVAREZ, L ;

GUICHARD, F ;

LIONS, PL ;

MOREL, JM .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1993, 123 (03) :199-257

[2] On the affine heat equation for non-convex curves [J].

Angenent, S ;

Sapiro, G ;

Tannenbaum, A .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 11 (03) :601-634

[3]

Bänsch E, 2001, NUMER MATH, V88, P203, DOI 10.1007/s002110000225

[4] A finite element method for surface diffusion:: the parametric case [J].

Bänsch, E ;

Morin, P ;

Nochetto, RH .

JOURNAL OF COMPUTATIONAL PHYSICS, 2005, 203 (01) :321-343

[5] A variational formulation of anisotropic geometric evolution equations in higher dimensions [J].

Barrett, John W. ;

Garcke, Harald ;

Nurnberg, Robert .

NUMERISCHE MATHEMATIK, 2008, 109 (01) :1-44

[6] On the variational approximation of combined second and fourth order geometric evolution equations [J].

Barrett, John W. ;

Garcke, Harald ;

Nuernberg, Robert .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2007, 29 (03) :1006-1041

[7] A parametric finite element method for fourth order geometric evolution equations [J].

Barrett, John W. ;

Garcke, Harald ;

Nuernberg, Robert .

JOURNAL OF COMPUTATIONAL PHYSICS, 2007, 222 (01) :441-467

[8]

BARRETT JW, 2007, 222007 U REG

[9] Axisymmetric surface diffusion: Dynamics and stability of self-similar pinchoff [J].

Bernoff, AJ ;

Bertozzi, AL ;

Witelski, TP .

JOURNAL OF STATISTICAL PHYSICS, 1998, 93 (3-4) :725-776

[10]

Deckelnick K, 2005, ACTA NUMER, V14, P139, DOI 10.1017/S0962492904000224

← 1 2 3 4 →