Free Access
Volume 39, Number 6, November-December 2005
Page(s) 1177 - 1202
Published online 15 November 2005
  1. S. Alinhac and P. Gérard, Opérateurs pseudo-différentiels et théorème de Nash-Moser, CNRS Éditions (1991). [Google Scholar]
  2. G.A. Baker, W.N. Jureidini and O.A. Karakashian, A piecewise solenoidal vector fields and the stokes problem. SIAM J. Numer. Anal. 27 (1990) 1466-1485. [CrossRef] [MathSciNet] [Google Scholar]
  3. D.S. Balsara and D.S. Spicer, A piecewise solenoidal vector fields and the stokes problem. J. Comput. Phys. 149 (1999) 270–292. [Google Scholar]
  4. J.U. Brackbill and D.C. Barnes. The effect of nonzero Formula on the numerical solution of the magnetohydrodynamic equations. J. Comput. Phys. 35 (1980) 426. [Google Scholar]
  5. P.G. Ciarlet, Basic error estimates for elliptic problems, in Handbook of numerical analysis, P.G. Ciarlet and J.-L. Lions, Eds., North-Holland (1991) 17–351. [Google Scholar]
  6. B. Cockburn, Discontinuous Galerkin methods for convection dominated problems, in High-order methods for computational physics, Springer, Berlin. Lect. Notes Comput. Sci. Eng. 9 (1999) 69–224. [Google Scholar]
  7. B. Cockburn, F. Li and C.-W. Shu, Locally divergence-free discontinuous Galerkin-methods for the Maxwell equations. J. Comput. Phys. 194 (2004) 588–610. [CrossRef] [MathSciNet] [Google Scholar]
  8. M. Costabel, A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains. Math. Method Appl. Sci. 12 (1990) 365–368. [Google Scholar]
  9. M. Costabel and M. Dauge, Un résultat de densité pour les équations de Maxwell régularisées dans un domaine lipschitzien. C. R. Acad. Sci. Paris Sér. I 327 849–854 (1998). [Google Scholar]
  10. W. Dai and P.R. Woodward, On the divergence-free condition and conservation laws in numerical simulations for supersonic magnetohydrodynamic flow. Astrophys. J. 494 (1998) 317. [Google Scholar]
  11. A. Dedner, F. Kemm, D. Kröner, C.-D. Munz, T. Schnitzer and M. Wesenberg, Hyperbolic Divergence cleaning for the MHD equations. J. Comput. Phys. 175 (2002) 645–673. [Google Scholar]
  12. C.R. Evans and J.F. Hawley, Simulation of magnetohydrodynamic flows, a constrained transport method. Astrophys. J. 332 (1988) 659. [Google Scholar]
  13. C. Foias and R. Temam, Remarques sur les équations de Navier-Stokes et les phénoménes successifs de bifurcation. Ann. Sci. Norm. Sup. Pisa Sér. IV 5 (1978) 29–63. [Google Scholar]
  14. K.O. Friedrichs, Symmetric positive linear differential equations. Comm. Pure Appl. Math. XI (1958) 333–418. [Google Scholar]
  15. V. Gilrault and P.-A. Raviart, Finite element methods for the Navier-Stokes equatons, Theory and algorithms. Springer Ser. Comput. Math. 5 (1986). [Google Scholar]
  16. O.A. Karakashian and W.N. Jureidini, A nonconforming finite element method for the stationary Navier-Stokes equations. SIAM J. Numer. Anal. 35 (1998) 93–120. [CrossRef] [MathSciNet] [Google Scholar]
  17. F. Li, C.-W. Shu, Locally divergence-free discontinuous Galerkin methods for MHD equations. SIAM J. Sci. Comput. 27 (2005) 413–442. [Google Scholar]
  18. J.-L. Lions and J. Petree, Sur une classe d'espaces d'interpolation. Publ. I.H.E.S. 19 (1964) 5–68. [Google Scholar]
  19. J.C. Nédélec, Mixed finite element in Formula . Numer. Math. 35 (1980) 315–341. [CrossRef] [MathSciNet] [Google Scholar]
  20. K.G. Powell, An approximate Riemann solver for magnetohydrodynamics (that works in more than one dimension), ICASE-Report 94-24 (NASA CR-194902), NASA Langley Research Center, Hampton, VA 23681-0001 (1994). [Google Scholar]
  21. P.-A. Raviart and J.M. Thomas, A mixed finite element method for 2nd order elliptic problems, Mathematical aspects of finite elements methods, in Proc. of the conference held in Rome, 10–12 Dec. 1975, A. Dold, B. Eckmann, Eds., Springer, Berlin, Heidelberg, New York. Lect. Notes Math. 606 (1977). [Google Scholar]
  22. G. Tóth, The Formula constraint in shock-capturing magnetohydrodynamics codes. J. Comput. Phys. 161 (2000) 605. [Google Scholar]
  23. L. Ying, A second order explicit finite element scheme to multidimensional conservation laws and its convergence. Sci. China Ser. A 43 (2000) 945–957. [CrossRef] [MathSciNet] [Google Scholar]
  24. Q. Zhang and C.-W. Shu, Error Estimates to smooth solutions of Runge-Kutta discontinuous Galerkin methods for scalar conservation laws. SIAM J. Numer. Anal. 42 (2004) 641–666. [Google Scholar]

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