Error estimates for approximations of a gradient dynamics for phase field elastic bending energy of vesicle membrane deformation

被引：3
作者：
Zhu, Liyong [1 ,2 ]
Du, Qiang [3 ]
机构：
[1] Beihang Univ, LMIB, Beijing 100191, Peoples R China
[2] Beihang Univ, Sch Math & Syst Sci, Beijing 100191, Peoples R China
[3] Penn State Univ, Dept Math, University Pk, PA 16802 USA
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2014年 / 37卷 / 06期
基金：
高等学校博士学科点专项科研基金; 中国国家自然科学基金;
关键词：
gradient flow; error estimates; mixed finite element; vesicle membrane; phase field; CAHN-HILLIARD EQUATION; FINITE-DIFFERENCE SCHEME; ELEMENT-METHOD; MODEL; SHAPES;
D O I：
10.1002/mma.2850
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the numerical approximations of a gradient flow associated with a phase field bending elasticity model of a vesicle membrane with prescribed volume and surface area. A spatially semi-discrete scheme based on a mixed finite element formulation and a fully discrete in space and time scheme are analyzed. Optimal order error estimates are rigorously derived for these numerical schemes without any a priori assumption. Copyright (c) 2013 John Wiley & Sons, Ltd.
引用
收藏
页码：913 / 930
页数：18
相关论文
共 33 条
  • [1] Adams A., 2003, Sobolev Spaces, V140
  • [2] Phase-field approach to three-dimensional vesicle dynamics
    Biben, T
    Kassner, K
    Misbah, C
    [J]. PHYSICAL REVIEW E, 2005, 72 (04):
  • [3] Brenner S. C., 2007, MATH THEORY FINITE E
  • [4] Brezzi F., 1991, Mixed and Hybrid Finite Element Methods, V15
  • [5] Model for curvature-driven pearling instability in membranes
    Campelo, F.
    Hernandez-Machado, A.
    [J]. PHYSICAL REVIEW LETTERS, 2007, 99 (08)
  • [6] Mapping vesicle shapes into the phase diagram: A comparison of experiment and theory
    Dobereiner, HG
    Evans, E
    Kraus, M
    Seifert, U
    Wortis, M
    [J]. PHYSICAL REVIEW E, 1997, 55 (04) : 4458 - 4474
  • [7] Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions
    Du, Q
    Liu, C
    Wang, XQ
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2006, 212 (02) : 757 - 777
  • [8] A phase field formulation of the Willmore problem
    Du, Q
    Liu, C
    Ryham, R
    Wang, XQ
    [J]. NONLINEARITY, 2005, 18 (03) : 1249 - 1267
  • [9] A phase field approach in the numerical study of the elastic bending energy for vesicle membranes
    Du, Q
    Liu, C
    Wang, XQ
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2004, 198 (02) : 450 - 468
  • [10] NUMERICAL-ANALYSIS OF A CONTINUUM MODEL OF PHASE-TRANSITION
    DU, Q
    NICOLAIDES, RA
    [J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1991, 28 (05) : 1310 - 1322
1234