Free Access
Volume 47, Number 6, November-December 2013
Page(s) 1713 - 1732
Published online 07 October 2013
  1. S. Agmon, Lectures on elliptic boundary value problems. Prepared for publication by B. Frank Jones, Jr. with the assistance of George W. Batten, Jr. Van Nostrand Mathematical Studies, No. 2. D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London (1965). [Google Scholar]
  2. M.S. Alnæs, A. Logg and K.-A. Mardal, UFC: a Finite Element Code Generation Interface, Chapt. 16. Springer (2012). [Google Scholar]
  3. D.N. Arnold, R.S. Falk and R. Winther, Finite element exterior calculus, homological techniques, and applications. Acta Numer. 15 (2006) 1–155. [CrossRef] [MathSciNet] [Google Scholar]
  4. D. Boffi, Approximation of eigenvalues in mixed form, discrete compactness property, and application to hp mixed finite elements. Comput. Meth. Appl. Mech. Eng. 196 (2007) 3672–3681. [Google Scholar]
  5. D. Boffi, F. Brezzi and L. Gastaldi, On the problem of spurious eigenvalues in the approximation of linear elliptic problems in mixed form. Math. Comput. 69 (2000) 121–140. [CrossRef] [MathSciNet] [Google Scholar]
  6. A. Bossavit, Extrusion, contraction: Their discretization via Whitney forms. COMPEL 22 (2004) 470–480. [Google Scholar]
  7. F. Brezzi, L.D. Marini and E. Süli, Discontinuous Galerkin methods for first-order hyperbolic problems. Math. Mod. Meth. Appl. Sci. 14 (2004) 1893–1903. [CrossRef] [MathSciNet] [Google Scholar]
  8. P. Castillo, B. Cockburn and I. Perugi and D. Schötzau, An a priori error analysis of the local discontinuous Galerkin method for elliptic problems. SIAM J. Numer. Anal. 38 (2000) 1676–1706. [CrossRef] [MathSciNet] [Google Scholar]
  9. M. Clemens, M. Wilke and T. Weiland, Advanced FI2TD algorithms for transient eddy current problems. COMPEL 20 (2001) 365–379. [CrossRef] [Google Scholar]
  10. A. Ern and J.-L. Guermond, Discontinuous Galerkin methods for Friedrichs’ systems. I. General theory. SIAM J. Numer. Anal. 44 (2006) 753–778. [CrossRef] [MathSciNet] [Google Scholar]
  11. R.S. Falk and G.R. Richter, Explicit finite element methods for symmetric hyperbolic equations. SIAM J. Numer. Anal. 36 (1999) 935–952 (electronic). [CrossRef] [Google Scholar]
  12. K.O. Friedrichs, Symmetric positive linear differential equations. Comm. Pure Appl. Math. 11 (1958) 333–418. [CrossRef] [MathSciNet] [Google Scholar]
  13. F.G. Fuchs, K.H. Karlsen, S. Mishra and N.H. Risebro, Stable upwind schemes for the magnetic induction equation. ESAIM: M2AN 43 (2009) 825–852. [CrossRef] [EDP Sciences] [Google Scholar]
  14. F. Henrotte, H. Heumann, E. Lange and K. Haymeyer, Upwind 3-d vector potential formulation for electromagnetic braking simulations. IEEE Trans. Magn. 46 (2010) 2835–2838. [CrossRef] [Google Scholar]
  15. H. Heumann, Eulerian and Semi-Lagrangian Methods for Advection-Diffusion of Differential Forms, Ph.D. thesis, ETH Zürich, Switzerland (2011). [Google Scholar]
  16. H. Heumann and R. Hiptmair, Eulerian and semi-Lagrangian methods for convection-diffusion for differential forms. Discrete Contin. Dyn. Syst. 29 (2011) 1471–1495. [CrossRef] [MathSciNet] [Google Scholar]
  17. R. Hiptmair, Finite elements in computational electromagnetism. Acta Numer. 11 237–339 (2002). [CrossRef] [MathSciNet] [Google Scholar]
  18. P. Houston, I. Perugia, A. Schneebeli and D. Schötzau, Interior penalty method for the indefinite time-harmonic Maxwell equations. Numer. Math. 100 (2005) 485–518. [CrossRef] [MathSciNet] [Google Scholar]
  19. P. Houston, I. Perugia, A. Schneebeli and D. Schötzau, Mixed discontinuous Galerkin approximation of the Maxwell operator: the indefinite case. ESAIM: M2AN 39 (2005) 727–753. [CrossRef] [EDP Sciences] [Google Scholar]
  20. P. Houston, I. Perugia and D. Schötzau, Mixed discontinuous Galerkin approximation of the Maxwell operator. SIAM J. Numer. Anal. 42 (2004) 434–459. [CrossRef] [MathSciNet] [Google Scholar]
  21. P. Houston, I. Perugia and D. Schötzau, Mixed discontinuous Galerkin approximation of the Maxwell operator: non-stabilized formulation. J. Sci. Comput. 22/23 (2005) 315–346. [CrossRef] [MathSciNet] [Google Scholar]
  22. P. Houston, C. Schwab and E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002) 2133–2163. [CrossRef] [MathSciNet] [Google Scholar]
  23. T.J.R. Hughes and A. Brooks, A multidimensional upwind scheme with no crosswind diffusion. In Finite Element Methods for Convection Dominated Flows, vol. 34 of AMD, Amer. Soc. Mech. Engrg. New York (1979) 19–35. [Google Scholar]
  24. T.J.R. Hughes, L.P. Franca and G.M. Hulbert, A new finite element formulation for computational fluid dynamics. VIII. The Galerkin/least-squares method for advective-diffusive equations. Comput. Methods Appl. Mech. Engrg. 73 (1989) 173–189. [CrossRef] [MathSciNet] [Google Scholar]
  25. M. Jensen, Discontinuous Galerkin Methods for Friedrichs Systems with Irregular Solutions. Ph.D. thesis, University of Oxford, England (2005). [Google Scholar]
  26. M. Jensen, On the discontinuous Galerkin method for Friedrichs systems in graph spaces. In Large-scale scientific computing. Lecture Notes in Comput. Sci., vol. 3743. Springer, Berlin (2006) 94–101. [Google Scholar]
  27. O.A. Karakashian and F. Pascal, A posteriori error estimates for a discontinuous Galerkin approximation of second-order elliptic problems. SIAM J. Numer. Anal. 41 (2003) 2374–2399 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  28. P. Lasaint and P.-A. Raviart, On a finite element method for solving the neutron transport equation, in Proc. Sympos., Math. Res. Center, Univ. of Wisconsin-Madison vol. 33. Academic Press, New York (1974) 89–123. [Google Scholar]
  29. A. Logg, G.N. Wells and J. Hake, DOLFIN: a C++/Python Finite Element Library, Chapt. 10. Springer (2012). [Google Scholar]
  30. P. Mullen, A. McKenzie, D. Pavlov, L. Durant, Y. Tong, E. Kanso, J. Marsden and M. Desbrun, Discrete Lie advection of differential forms. Foundations of Computational Mathematics 11 (2011) 131–149. [Google Scholar]
  31. J.-C. Nédélec, Mixed finite elements in R3. Numer. Math. 35 (1980) 315–341. [CrossRef] [MathSciNet] [Google Scholar]
  32. J.-C. Nédélec, A new family of mixed finite elements in R3. Numer. Math. 50 (1986) 57–81. [CrossRef] [MathSciNet] [Google Scholar]
  33. T.E. Peterson, A note on the convergence of the discontinuous Galerkin method for a scalar hyperbolic equation. SIAM J. Numer. Anal. 28 (1991) 133–140. [CrossRef] [MathSciNet] [Google Scholar]
  34. W.H. Reed and T. R. Hill, Triangular mesh methods for the neutron transport equation. Tech. Rep. LA-UR-73-479, Los Alamos National Laboratory, Los Alamos, NM (1973). [Google Scholar]
  35. G.R. Richter, An optimal-order error estimate for the discontinuous Galerkin method. Math. Comput. 50 (1988) 75–88. [CrossRef] [Google Scholar]
  36. H.-G. Roos, M. Stynes and L. Tobiska, Robust numerical methods for singularly perturbed differential equations, Convection-diffusion-reaction and flow problems, volume 24 of Springer Series in Computational Mathematics. 2nd edition. Springer-Verlag, Berlin (2008). [Google Scholar]
  37. G. Zhou, How accurate is the streamline diffusion finite element method? Math. Comput. 66 (1997) 31–44. [CrossRef] [Google Scholar]

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