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Error estimates for approximations of a gradient dynamics for phase field elastic bending energy of vesicle membrane deformation
Author(s) -
Zhu Liyong,
Du Qiang
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2850
Subject(s) - mathematics , elasticity (physics) , finite element method , a priori and a posteriori , bending , balanced flow , phase field models , mathematical analysis , deformation (meteorology) , phase (matter) , physics , philosophy , epistemology , quantum mechanics , meteorology , thermodynamics
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 © 2013 John Wiley & Sons, Ltd.