Free Access
Issue
ESAIM: M2AN
Volume 49, Number 5, September-October 2015
Page(s) 1303 - 1330
DOI https://doi.org/10.1051/m2an/2015013
Published online 18 August 2015
  1. A. Alphonse, C. Elliott and B. Stinner, An abstract framework for parabolic pdes on evolving spaces. Port. Math. 72 (2015) 1–46. [CrossRef] [MathSciNet] [Google Scholar]
  2. A. Bonito, R. Nochetto and M. Pauletti, Dynamics of biomembranes: effect of the bulk fluid. Math. Model. Nat. Phenom. 6 (2011) 25–43. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  3. E. Burman and P. Hansbo, Fictitious domain finite element methods using cut elements: II. A stabilized nitsche method. Appl. Numer. Math. 62 (2012) 328–341. [CrossRef] [MathSciNet] [Google Scholar]
  4. E. Burman, P. Hansbo, M. Larson and S. Zahedi, Cut finite element methods for coupled bulk-surface problems. Preprint (2014) arXiv:1403.6580. [Google Scholar]
  5. L. Cattaneo, L. Formaggia, G.F. Iori, A. Scotti and P. Zunino,Stabilized extended finite elements for the approximation of saddle point problems with unfitted interfaces. Calcolo (2014) 1–30. [Google Scholar]
  6. K.-Y. Chen and M.-C. Lai, A conservative scheme for solving coupled surface-bulk convection-diffusion equations with an application to interfacial flows with soluble surfactant. J. Comput. Phys. 257 (2014) 1–18. [CrossRef] [Google Scholar]
  7. J. Chessa and T. Belytschko, An extended finite element method for two-phase fluids. ASME J. Appl. Mech. 70 (2003) 10–17. [CrossRef] [MathSciNet] [Google Scholar]
  8. R. Clift, J. Grace and M. Weber, Bubbles, Drops and Particles. Dover, Mineola (2005). [Google Scholar]
  9. K. Deckelnick, C.M. Elliott and T. Ranner, Unfitted finite element methods using bulk meshes for surface partial differential equations. SIAM J. Numer. Anal. 52 (2014) 2137–2162. [CrossRef] [Google Scholar]
  10. A. Demlow, Higher-order finite element methods and pointwise error estimates for elliptic problems on surfaces. SIAM J. Numer. Anal. 47 (2009) 805–827. [CrossRef] [MathSciNet] [Google Scholar]
  11. A. Demlow and G. Dziuk, An adaptive finite element method for the Laplace−Beltrami operator on implicitly defined surfaces. SIAM J. Numer. Anal. 45 (2007) 421–442. [CrossRef] [MathSciNet] [Google Scholar]
  12. A. Demlow and M. Olshanskii, An adaptive surface finite element method based on volume meshes. SIAM J. Numer. Anal. 50 (2012) 1624–1647. [CrossRef] [Google Scholar]
  13. M. Do-Quang, G. Amberg and C.-O. Petterson, Modeling of the adsorption kinetics and the convection of surfactants in a weld pool. J. Heat Transfer 130 (2008) 092102–1. [CrossRef] [Google Scholar]
  14. G. Dziuk and C. Elliott, Finite element methods for surface pdes. Acta Numer. 22 (2013) 289–396. [CrossRef] [MathSciNet] [Google Scholar]
  15. C. Eggleton and K. Stebe, An adsorption-desorption-controlled surfactant on a deforming droplet. J. Colloid Interface Sci. 208 (1998) 68–80. [CrossRef] [PubMed] [Google Scholar]
  16. C. Elliott and T. Ranner, Finite element analysis for a coupled bulk-surface partial differential equation. IMA J. Numer. Anal. 33 (2013) 377–402. [CrossRef] [MathSciNet] [Google Scholar]
  17. A. Ern and J.-L. Guermond, Theory and practice of finite elements. Springer, New York (2004). [Google Scholar]
  18. T. Fries and T. Belytschko, The generalized/extended finite element method: An overview of the method and its applications. Int. J. Num. Meth. Eng. 84 (2010) 253–304. [Google Scholar]
  19. J. Grande and A. Reusken, A higher order finite element method for partial differential equations on surfaces. IGPM RWTH Aachen University. Preprint 403 (2014). [Google Scholar]
  20. P. Grisvard, Elliptic problems in nonsmooth domains. Pitman, Boston (1985). [Google Scholar]
  21. S. Gross, M.A. Olshanskii and A. Reusken, A trace finite element method for a class of coupled bulk-interface transport problems. SC&NA, University of Houston. Preprint 28 (2014). [Google Scholar]
  22. S. Gross and A. Reusken, An extended pressure finite element space for two-phase incompressible flows with surface tension. J. Comput. Phys. 224 (2007) 40–58. [CrossRef] [Google Scholar]
  23. S. Gross and A. Reusken, Numerical Methods for Two-phase Incompressible Flows. Springer, Berlin (2011). [Google Scholar]
  24. A. Hansbo and P. Hansbo, An unfitted finite element method, based on nitsche’s method, for elliptic interface problems. Comput. Methods Appl. Mech. Engrg. 191 (2002) 5537–5552. [CrossRef] [MathSciNet] [Google Scholar]
  25. A. Hansbo and P. Hansbo, A finite element method for the simulation of strong and weak discontinuities in solid mechanics. Comput. Methods Appl. Mech. Engrg. 193 (2004) 3523–3540. [CrossRef] [MathSciNet] [Google Scholar]
  26. P. Hansbo, M.G. Larson and S. Zahedi, A cut finite element method for a stokes interface problem. Appl. Numer. Math. 85 (2014) 90–114. [CrossRef] [Google Scholar]
  27. M. Olshanskii and A. Reusken, A finite element method for surface PDEs: matrix properties. Numer. Math. 114 (2009) 491–520. [CrossRef] [Google Scholar]
  28. M. Olshanskii and A. Reusken, Error analysis of a space-time finite element method for solving PDEs on evolving surfaces, SIAM J. Numer. Anal. 52 (2014) 2092–2120. [CrossRef] [Google Scholar]
  29. M. Olshanskii, A. Reusken and J. Grande, A finite element method for elliptic equations on surfaces. SIAM J. Numer. Anal. 47 (2009) 3339–3358. [CrossRef] [Google Scholar]
  30. M. Olshanskii, A. Reusken and X. Xu, An Eulerian space-time finite element method for diffusion problems on evolving surfaces. SIAM J. Numer. Anal. 52 (2014) 1354–1377. [CrossRef] [Google Scholar]
  31. M. Olshanskii, A. Reusken and X. Xu, A stabilized finite element method for advection-diffusion equations on surfaces. IMA J. Numer. Anal. 34 (2014) 732–758. [CrossRef] [MathSciNet] [Google Scholar]
  32. M. Olshanskii and D. Safin, A narrow-band unfitted finite element method for elliptic pdes posed on surfaces. To appear in Math. Comput. (2015). [Google Scholar]
  33. F. Ravera, M. Ferrari and L. Liggieri, Adsorption and partition of surfactants in liquid-liquid systems. Adv. Colloid Interface Sci. 88 (2000) 129–177. [CrossRef] [PubMed] [Google Scholar]
  34. A. Reusken, Analysis of trace finite element methods for surface partial differential equations. To appear in IMA J. Numer. Anal. (2014). Doi: 10.1093/imanum/dru047. [Google Scholar]
  35. S. Tasoglu, U. Demirci and M. Muradoglu, The effect of soluble surfactant on the transient motion of a buoyancy-driven bubble. Physics of Fluids 20 (2008) 040805–1. [CrossRef] [Google Scholar]
  36. J. Wloka, Partial Differential Equations. Cambridge University Press, Cambridge (1987). [Google Scholar]

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