TY - JOUR
T1 - Convergence of Numerical Approximations to a Phase Field Bending Elasticity Model of Membrane Deformations
AU - Q. Du & X. Wang
JO - International Journal of Numerical Analysis and Modeling
VL - 3-4
SP - 441
EP - 459
PY - 2007
DA - 2007/04
SN - 4
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/871.html
KW - numerical approximations, finite element, mixed finite element, phase field model, membrane deformation, elastic bending energy, gradient flow, convergence analysis.
AB - <p style="text-align: justify;">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.</p>