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Volume 4, Issue 3-4
Convergence of Numerical Approximations to a Phase Field Bending Elasticity Model of Membrane Deformations

Q. Du & X. Wang

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

Published online: 2007-04

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  • 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.

  • Keywords

numerical approximations, finite element, mixed finite element, phase field model, membrane deformation, elastic bending energy, gradient flow, convergence analysis.

  • AMS Subject Headings

65N12, 65M12, 65N30, 65M60, 49J45, 92C37, 92C05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-4-441, author = {Q. Du and X. Wang}, title = {Convergence of Numerical Approximations to a Phase Field Bending Elasticity Model of Membrane Deformations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2007}, volume = {4}, number = {3-4}, pages = {441--459}, 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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/871.html} }
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 -

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.

Q. Du and X. Wang. (2007). Convergence of Numerical Approximations to a Phase Field Bending Elasticity Model of Membrane Deformations. International Journal of Numerical Analysis and Modeling. 4 (3-4). 441-459. doi:
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