Free Access
Math. Model. Nat. Phenom.
Volume 6, Number 5, 2011
Complex Fluids
Page(s) 25 - 43
Published online 10 August 2011
  1. R.A. Adams, J.J.F. Fournier. Sobolev spaces. Pure and Applied Mathematics, second edition, Amsterdam, 2003.
  2. E. Bänsch. Finite element discretization of the Navier-Stokes equations with a free capillary surface. Numer. Math., 88 (2001), No. 2, 203–235. [CrossRef] [MathSciNet]
  3. E. Bänsch, P. Morin, R.H. Nochetto. A finite element method for surface diffusion: the parametric case. J. Comput. Phys., 203 (2005), No. 1, 321–343. [CrossRef] [MathSciNet]
  4. J.W. Barrett, H. Garcke, R. Nürnberg. Parametric approximation of Willmore flow and related geometric evolution equations. SIAM J. Sci. Comput., 31 (2008), No. 1, 225–253. [CrossRef] [MathSciNet]
  5. A. Bonito, R. H. Nochetto, M. S. Pauletti. Geometrically consistent mesh modification. SIAM J. Numer. Anal., 48 (2010), No. 5, 1877–1899. [CrossRef] [MathSciNet]
  6. A. Bonito, R.H. Nochetto, M.S. Pauletti. Parametric fem for geometric biomembranes. J. Comput. Phys., 229 (2010), No. 9, 3171–3188. [CrossRef] [MathSciNet]
  7. P.B. Canham. The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell. Journal of Theoretical Biology, 26 (1970), No. 1, 61–81. [CrossRef] [PubMed]
  8. P.G. Ciarlet, J.-L. Lions, editors. Finite element methods. Part 1. Handbook of numerical analysis, 2, North-Holland, Amsterdam, 1991.
  9. U. Clarenz, U. Diewald, G. Dziuk, M. Rumpf, R. Rusu. A finite element method for surface restoration with smooth boundary conditions. Comput. Aided Geom. Design, 21 (2004), No. 5, 427–445. [MathSciNet]
  10. T.A. Davis. Algorithm 832: UMFPACK V4.3—an unsymmetric-pattern multifrontal method. ACM Trans. Math. Software, 30 (2004), No. 2, 196–199. [CrossRef] [MathSciNet]
  11. K. Deckelnick, G. Dziuk. Error analysis of a finite element method for the Willmore flow of graphs. Interfaces Free Bound., 8 (2006), No. 1, 21–46. [CrossRef] [MathSciNet]
  12. K. Deckelnick, G. Dziuk, C.M. Elliott. Computation of geometric partial differential equations and mean curvature flow. Acta Numer., 14 (2005), 139–232. [CrossRef] [MathSciNet]
  13. M.C. Delfour, J.-P. Zolésio. Shapes and geometries. Advances in Design and Control, Society for Industrial and Applied Mathematics, Philadelphia, PA, 2001.
  14. A. Demlow. Higher-order finite element methods and pointwise error estimates for elliptic problems on surfaces. SIAM J. Numer. Anal., 47 (2009), No. 2, 805–827. [CrossRef] [MathSciNet]
  15. G. Doǧan, P. Morin, R.H. Nochetto, M. Verani. Discrete gradient flows for shape optimization and applications. Comput. Methods Appl. Mech. Engrg., 196 (2007), No. 37-40, 3898–3914. [CrossRef] [MathSciNet]
  16. M. Droske, M. Rumpf. A level set formulation for Willmore flow. Interfaces Free Bound., 6 (2004), No. 3, 361–378. [CrossRef] [MathSciNet]
  17. Q. Du, C. Liu, X. Wang. A phase field approach in the numerical study of the elastic bending energy for vesicle membranes. J. Comput. Phys., 198 (2004), No. 2, 450–468. [CrossRef] [MathSciNet]
  18. Q. Du, C. Liu, X. Wang. Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions. J. Comput. Phys., 212 (2006), No. 2, 757–777. [CrossRef] [MathSciNet]
  19. Q. Du, Ch. Liu, R. Ryham, X. Wang. Energetic variational approaches in modeling vesicle and fluid interactions. Physica D, 238 (2009), No. 9-10, 923–930. [CrossRef] [MathSciNet]
  20. G. Dziuk. An algorithm for evolutionary surfaces. Numer. Math., 58 (1991), No. 6, 603–611. [CrossRef] [MathSciNet]
  21. G. Dziuk. Computational parametric willmore flow. Numer. Math., 111 (2008), No. 1, 55–80. [CrossRef] [MathSciNet]
  22. S. Esedoglu, S.J. Ruuth, R. Tsai. Threshold dynamics for high order geometric motions. Interfaces Free Bound., 10 (2008), No. 3, 263–282. [CrossRef] [MathSciNet]
  23. E.A. Evans, R. Skalak. Mechanics and thermodynamics of biomembranes .2. CRC Critical reviews in bioengineering, 3 (1979), No. 4, 331–418. [PubMed]
  24. M. Giaquinta, S. Hildebrandt. Calculus of variations. I, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 310, Springer-Verlag, Berlin, 1996.
  25. W. Helfrich. Elastic properties of lipid bilayers - theory and possible experiments. Zeitschrift Fur Naturforschung C-A Journal Of Biosciences, 28 (1973), 693.
  26. D. Hu, P. Zhang, W. E. Continuum theory of a moving membrane. Phys. Rev. E (3), 75 (2007), No. 4, 11.
  27. J.T. Jenkins. The equations of mechanical equilibrium of a model membrane. SIAM J. Appl. Math., 32 (1977), No. 4, 755–764. [CrossRef] [MathSciNet]
  28. D. Köster, O. Kriessl, K.G. Siebert. Design of finite element tools for coupled surface and volume meshes. Numer. Math. Theor. Meth. Appl., 1 (2008), No. 3, 245–274.
  29. W. Losert. Personal communication, 2009.
  30. M.S. Pauletti. Parametric AFEM for geometric evolution equation and coupled fluid-membrane interaction. Thesis (Ph.D.)–University of Maryland, College Park, 2008.
  31. R.E. Rusu. An algorithm for the elastic flow of surfaces. Interfaces Free Bound., 7 (2005), No. 3, 229–239. [CrossRef] [MathSciNet]
  32. A. Schmidt, K.G. Siebert. Design of adaptive finite element software: The finite element toolbox ALBERTA, Lecture Notes in Computational Science and Engineering, 42, Springer-Verlag, Berlin, 2005.
  33. U. Seifert. Configurations of fluid membranes and vesicles. Advances in Physics, 46 (1997), No. 1, 13–137. [CrossRef]
  34. D.J. Steigmann. Fluid films with curvature elasticity. Arch. Ration. Mech. Anal., 150 (1999), No. 2, 127–152. [CrossRef] [MathSciNet]
  35. D.J. Steigmann, E. Baesu, R.E. Rudd, J. Belak, M. McElfresh. On the variational theory of cell-membrane equilibria. Interfaces Free Bound., 5 (2003), No. 4, 357–366. [CrossRef] [MathSciNet]
  36. R. Temam. Navier-Stokes equations. Theory and numerical analysis. North-Holland Publishing Co., Amsterdam, 1977.

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.