Free Access
Issue
ESAIM: M2AN
Volume 42, Number 6, November-December 2008
Page(s) 1065 - 1087
DOI https://doi.org/10.1051/m2an:2008034
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] [Google Scholar]
  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] [Google Scholar]
  3. L. Banas and A. Prohl, Convergent finite element discretization of the multi-fluid nonstationary incompressible magnetohydrodynamics equations. (In preparation). [Google Scholar]
  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] [Google Scholar]
  5. S.C. Brenner and L.R. Scott, The mathematical theory of finite element methods. Springer (1994). [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  8. A.J. Chorin, Numercial solution of the Navier-Stokes equations. Math. Comp. 22 (1968) 745–762. [CrossRef] [MathSciNet] [Google Scholar]
  9. M. Costabel and M. Dauge, Weighted regularization of Maxwell equations in polyhedral domains. Numer. Math. 93 (2002) 239–277. [CrossRef] [MathSciNet] [Google Scholar]
  10. V. Georgescu, Some boundary value problems for differential forms on compact Riemannian manifolds. Ann. Math. Pura Appl. 122 (1979) 159–198. [CrossRef] [Google Scholar]
  11. J.-F. Gerbeau, A stabilized finite element method for the incompressible magnetohydrodynamic equations. Numer. Math. 87 (2000) 83–111. [CrossRef] [MathSciNet] [Google Scholar]
  12. J.-F. Gerbeau, C. Le Bris and T. Lelievre, Mathematical methods for the magnetohydrodynamics of liquid crystals. Oxford Science Publication (2006). [Google Scholar]
  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] [Google Scholar]
  14. V. Girault and P.-A. Raviart, Finite element methods for Navier-Stokes equations. Springer (1986). [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  18. R. Hiptmair, Finite elements in computational electromagnetism. Acta Numer. 11 (2002) 237–339. [CrossRef] [MathSciNet] [Google Scholar]
  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] [Google Scholar]
  20. F. Kikuchi, On a discrete compactness property for the Nédélec finite elements. J. Fac. Sci. Univ. Tokyo Sec. IA 36 (1989) 479–490. [Google Scholar]
  21. P. Monk, Finite element methods for Maxwell's equations. Oxford University Press, New York (2003). [Google Scholar]
  22. A. Prohl, Projection and quasi-compressibility methods for solving the incompressible Navier-Stokes equations. Teubner-Verlag, Stuttgart (1997). [Google Scholar]
  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] [Google Scholar]
  24. A. Prohl, On pressure approximation via projection methods for nonstationary incompressible Navier-Stokes equations. SIAM J. Numer. Anal. (to appear). [Google Scholar]
  25. D. Schötzau, Mixed finite element methods for stationary incompressible magneto-hydrodynamics. Numer. Math. 96 (2004) 771–800. [CrossRef] [MathSciNet] [Google Scholar]
  26. M. Sermange and R. Temam, Some mathematical questions related to the MHD equations. Comm. Pure Appl. Math. 36 (1983) 635–664. [CrossRef] [MathSciNet] [Google Scholar]
  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. [Google Scholar]
  28. J. Zhao, Analysis of finite element approximation for time-dependent Maxwell problems. Math. Comp. 73 (2003) 1089–1105. [CrossRef] [Google Scholar]

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