Free Access
Volume 42, Number 6, November-December 2008
Page(s) 1065 - 1087
Published online 12 August 2008
  1. C. Amrouche, C. Bernardi, M. Dauge and V. Girault, Vector potentials in three-dimensional nonsmooth domains. Math. Meth. Appl. Sci. 21 (1998) 823–864. [CrossRef] [MathSciNet]
  2. F. Armero and J.C. Simo, Long-time dissipativity of time-stepping algorithms for an abstract evolution equation with applications to the incompressible MHD and Navier-Stokes equations. Comp. Meth. Appl. Mech. Engrg. 131 (1996) 41–90. [CrossRef]
  3. L. Banas and A. Prohl, Convergent finite element discretization of the multi-fluid nonstationary incompressible magnetohydrodynamics equations. (In preparation).
  4. D. Boffi, P. Fernandes, L. Gastaldi and I. Perugia, Computational models of electromagnetic resonators: analysis of edge element approximation. SIAM J. Numer. Anal. 36 (1999) 1264–1290. [CrossRef] [MathSciNet]
  5. S.C. Brenner and L.R. Scott, The mathematical theory of finite element methods. Springer (1994).
  6. L. Cattabriga, Su un problema al contorno relativo al sistemo di equazioni di Stokes. Rend. Sem Mat. Univ. Padova 31 (1961) 308–340. [MathSciNet]
  7. Z. Chen, Q. Du and J. Zou, Finite element methods with matching and nonmatching meshes for Maxwell equations with discontinuous coefficients. SIAM J. Numer. Anal. 37 (2000) 1542–1570. [CrossRef] [MathSciNet] [PubMed]
  8. A.J. Chorin, Numercial solution of the Navier-Stokes equations. Math. Comp. 22 (1968) 745–762. [CrossRef] [MathSciNet]
  9. M. Costabel and M. Dauge, Weighted regularization of Maxwell equations in polyhedral domains. Numer. Math. 93 (2002) 239–277. [CrossRef] [MathSciNet]
  10. V. Georgescu, Some boundary value problems for differential forms on compact Riemannian manifolds. Ann. Math. Pura Appl. 122 (1979) 159–198. [CrossRef]
  11. J.-F. Gerbeau, A stabilized finite element method for the incompressible magnetohydrodynamic equations. Numer. Math. 87 (2000) 83–111. [CrossRef] [MathSciNet]
  12. J.-F. Gerbeau, C. Le Bris and T. Lelievre, Mathematical methods for the magnetohydrodynamics of liquid crystals. Oxford Science Publication (2006).
  13. V. Girault, R.H. Nochetto and R. Scott, Maximum-norm stability of the finite element Stokes projection. J. Math. Pures Appl. 84 (2005) 279–330. [CrossRef] [MathSciNet]
  14. V. Girault and P.-A. Raviart, Finite element methods for Navier-Stokes equations. Springer (1986).
  15. M.D. Gunzburger, A.J. Meir and J.S. Peterson, On the existence and uniqueness and finite element approximation of solutions of the equations of stationary incompressible magnetohydrodynamics. Math. Comp. 56 (1991) 523–563. [CrossRef] [MathSciNet]
  16. U. Hasler, A. Schneebeli and D. Schötzau, Mixed finite element approximation of incompressible MHD problems based on weighted regularization. Appl. Numer. Math. 51 (2004) 19–45. [CrossRef] [MathSciNet]
  17. J.G. Heywood and R. Rannacher, Finite element solution of the nonstationary 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]
  18. R. Hiptmair, Finite elements in computational electromagnetism. Acta Numer. 11 (2002) 237–339. [CrossRef] [MathSciNet]
  19. T.J.R. Hughes, L.P. Franca and M. Balestra, A new finite element formulation for computational fluid mechanics: V. Circumventing the Babuska-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accommodating equal order interpolation. Comp. Meth. Appl. Mech. Eng. 59 (1986) 85–99. [CrossRef] [MathSciNet]
  20. F. Kikuchi, On a discrete compactness property for the Nédélec finite elements. J. Fac. Sci. Univ. Tokyo Sec. IA 36 (1989) 479–490.
  21. P. Monk, Finite element methods for Maxwell's equations. Oxford University Press, New York (2003).
  22. A. Prohl, Projection and quasi-compressibility methods for solving the incompressible Navier-Stokes equations. Teubner-Verlag, Stuttgart (1997).
  23. A. Prohl, On the pollution effect of quasi-compressibility methods in magneto-hydrodynamics and reactive flows. Math. Meth. Appl. Sci. 22 (1999) 1555–1584. [CrossRef]
  24. A. Prohl, On pressure approximation via projection methods for nonstationary incompressible Navier-Stokes equations. SIAM J. Numer. Anal. (to appear).
  25. D. Schötzau, Mixed finite element methods for stationary incompressible magneto-hydrodynamics. Numer. Math. 96 (2004) 771–800. [CrossRef] [MathSciNet]
  26. M. Sermange and R. Temam, Some mathematical questions related to the MHD equations. Comm. Pure Appl. Math. 36 (1983) 635–664. [CrossRef] [MathSciNet]
  27. R. Temam, Sur l'approximation de la solutoin des equations de Navier-Stokes par la méthode de pas fractionnaires II. Arch. Rat. Mech. Anal. 33 (1969) 377–385.
  28. J. Zhao, Analysis of finite element approximation for time-dependent Maxwell problems. Math. Comp. 73 (2003) 1089–1105. [CrossRef]

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