Convergence of numerical approximations to a phase field bending elasticity model of membrane deformations

被引：0
作者：
Du, Qiang [1 ]
Wang, Xiaoqiang
机构：
[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA
[2] Univ Minnesota, Inst Math & Applicat, Minneapolis, MN 55455 USA
来源：
INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING | 2007年 / 4卷 / 3-4期
关键词：
numerical approximations; finite element; mixed finite element; phase field model; membrane deformation; elastic bending energy; gradient flow; convergence analysis;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study numerical approximations of a recently proposed phase field model for the vesicle membrane deformations governed by the variation of the elastic bending energy. Both the spatial discretization for the equilibrium problem with given volume and surface area constraints and the time discretization of a dynamic problem via gradient flow are considered. Convergence results of the numerical approximations are proved.
引用
收藏
页码：441 / 459
页数：19
相关论文
共 50 条
  • [41] Numerical simulations of the dynamics of axisymmetric compound liquid threads with a phase-field model
    Yang, Junxiang
    Li, Yibao
    Lee, Chaeyoung
    Kim, Junseok
    EUROPEAN JOURNAL OF MECHANICS B-FLUIDS, 2021, 89 : 203 - 216
  • [42] A Numerical procedure for solving 2D phase-field model problems
    Xu, Ying
    McDonough, J. M.
    Tagavi, K. A.
    JOURNAL OF COMPUTATIONAL PHYSICS, 2006, 218 (02) : 770 - 793
  • [43] Numerical prediction of the secondary dendrite arm spacing using a phase-field model
    Ode, M
    Kim, SG
    Kim, WT
    Suzuki, T
    ISIJ INTERNATIONAL, 2001, 41 (04) : 345 - 349
  • [44] Evaluation of fracture in mortar subject to tension loading using phase field model and three point bending test
    Ge, Zhi
    Wang, Yuanyuan
    Hou, Yue
    Sun, Wenjuan
    Sun, Renjuan
    MATERIALS & DESIGN, 2015, 86 : 121 - 128
  • [45] THREE-DIMENSIONAL NUMERICAL SIMULATIONS OF A PHASE-FIELD MODEL FOR ANISOTROPIC INTERFACIAL ENERGY
    Kim, Junseok
    COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2007, 22 (03): : 453 - 464
  • [46] A new approach to phase-field model for the phase separation dynamics in polymer membrane formation by immersion precipitation method
    Padilha Junior, Erli Jose
    Staudt, Paula Bettio
    Tessaro, Isabel Cristina
    Medeiros Cardozo, Nilo Sergio
    POLYMER, 2020, 186
  • [47] Phase-field simulations of ferro-electro-elasticity in model polycrystals with implications for phenomenological descriptions of bulk perovskite ceramics
    Indergand, Roman
    Kochmann, Dennis M.
    Idiart, Martin I.
    JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 2024, 192
  • [48] A central compact scheme for numerical solution of two-phase incompressible flow using Allen–Cahn phase field model
    Muhammad Rizwan
    Abdullah Shah
    Li Yuan
    Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2016, 38 : 433 - 441
  • [49] Phase field numerical model for simulating the diffusion controlled stress corrosion cracking phenomena in anisotropic material
    Mathew, Christian C.
    Song, Jie
    Adu-Gyamfi, Emmanuel
    Fu, Yao
    COMPUTATIONAL MATERIALS SCIENCE, 2025, 247
  • [50] Study on the elastoplastic damage model for rock based on the phase-field method and its numerical implementation
    Liu S.
    Wang W.
    Cao Y.
    Zhu Q.
    Shao J.
    Yanshilixue Yu Gongcheng Xuebao/Chinese Journal of Rock Mechanics and Engineering, 2023, 42 (04): : 896 - 905
12345