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

Zhu Liyong | Zendy; Du Qiang | Zendy

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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.

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