Int. J. Numer. Anal. Mod., 4 (2007), pp. 441-459.


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

Qiang Du 1, Xiaoqiang Wang 2

1 Department of Mathematics, Penn State University, University Park, PA 16802, USA
2 Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN 55455, USA

Received by the editors February 9, 2006, and, in revised form, March 6, 2006
Abstract

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.

AMS subject classifications: 65N12, 65M12, 65N30, 65M60, 49J45, 92C37, 92C05
Key words: numerical approximations; finite element; mixed finite element; phase field model; membrane deformation; elastic bending energy; gradient flow; convergence analysis
Email: qdu@math.psu.edu (Q. Du), wang@ima.umn.edu (X. Wang)
 

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