Free Access
Volume 44, Number 3, May-June 2010
Page(s) 531 - 571
Published online 23 February 2010
  1. R.A. Adams and J.J.F. Fournier, Sobolev Spaces. Elsevier (2003).
  2. D.N. Arnold, F. Brezzi and M. Fortin, A stable finite element for the Stokes equations. Calcolo 23 (1984) 337–344. [CrossRef] [MathSciNet]
  3. M.Z. Bazant, K. Thornton and A. Ajdari, Diffuse-charge dynamics in electrochemical systems. Phys. Rev. E 70 (2004) 021506. [CrossRef]
  4. S.C. Brenner and L. Scott, The Mathematical Theory of Finite Element Methods. Second edition, Springer (2002).
  5. A. Chorin, On the convergence of discrete approximations of the Navier-Stokes Equations. Math. Com. 23 (1969) 341–353. [CrossRef]
  6. P.G. Ciarlet and P.A. Raviart, Maximum principle and uniform convergence for the finite element method. Comput. Methods Appl. Mech. Eng. 2 (1973) 17–31. [CrossRef] [MathSciNet]
  7. J.F. Ciavaldini, Analyse numérique d'un problème de Stefan à deux phases par une méthode d'éléments finis. SIAM J. Numer. Anal. 12 (1975) 464–487. [CrossRef] [MathSciNet]
  8. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman Advanced Publishing Program, Boston, USA (1985).
  9. J.L. Guermond, J. Minev and J. Shen, An overview of projection methods for incompressible flows. Comput. Meth. Appl. Mech. Engrg. 195 (2006) 6011–6045. [CrossRef] [MathSciNet]
  10. J.G. Heywood and R. Rannacher, Finite element approximation of the non-stationary Navier-Stokes problem I: Regularity of solutions and second-order error estimates for spatial discretization. SIAM J. Numer. Anal. 19 (1982) 275–311. [CrossRef] [MathSciNet]
  11. R.J. Hunter, Foundations of Colloidal Science. Oxford University Press, UK (2000).
  12. M.S. Kilic, M.Z. Bazant and A. Ajdari, Steric effects in the dynamics of electrolytes at large applied voltages. II. Modified Poisson-Nernst-Planck equations. Phys. Rev. E 75 (2007) 021503. [CrossRef]
  13. J.L. Lions, On some questions in boundary value problems of mathematical physics, in Contemporary Developments in Continuum Mechanics and Partial Differential equations, Math. Stud. 30, Amsterdam, North-Holland (1978) 283–346.
  14. J.L. Lions and E. Magenes, Nonhomogeneous boundary value problems and applications, Grundlehren der Mathematischen Wissenschaften 181. Springer-Verlag, Berlin-New York (1972).
  15. P.L. Lions, Mathematical Topics in Fluid Mechanics, Volume 1: Incompressible Models. Oxford University Press, UK (1996).
  16. R.H. Nochetto and C. Verdi, Convergence past singularities for a fully discrete approximation of curvature-driven interfaces. SIAM J. Numer. Anal. 34 (1997) 490–512. [CrossRef] [MathSciNet]
  17. R.F. Probstein, Physiochemical Hydrodynamics, An introduction. John Wiley and Sons, Inc. (1994).
  18. A. Prohl, Projection and Quasi-Compressibility Methods for Solving the Incompressible Navier-Stokes Equations. Teubner (1997).
  19. A. Prohl, On pressure approximation via projection methods for the nonstationary incompressible Navier-Stokes equations. SIAM J. Numer. Anal. 47 (2008) 158–180. [CrossRef] [MathSciNet]
  20. A. Prohl and M. Schmuck, Convergent discretizations for the Nernst-Planck-Poisson system. Numer. Math. 111 (2009) 591–630. [CrossRef] [MathSciNet]
  21. M. Schmuck, Modeling, Analysis and Numerics in Electrohydrodynamics. Ph.D. Thesis, University of Tübingen, Germany (2008).
  22. M. Schmuck, Analysis of the Navier-Stokes-Nernst-Planck-Poisson system. M3AS 19 (2009) 1–23.
  23. J. Simon, Sobolev, Besov and Nikolskii fractional spaces: Imbeddings and comparisons for vector valued spaces on an interval. Ann. Mat. Pura Appl. 157 (1990) 117–148. [CrossRef] [MathSciNet]
  24. R. Temam, Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires ii. Arch. Ration. Mech. Anal. 33 (1969) 377–385.
  25. R. Temam, Navier-Stokes equations – theory and numerical analysis. AMS Chelsea Publishing, Providence, USA (2001).

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.

Recommended for you