Free Access
Volume 45, Number 4, July-August 2011
Page(s) 739 - 760
Published online 21 February 2011
  1. R.A Adams and J.J.F. Fournier, Sobolev SpacesPure and Applied Mathematics Series. Second edition, Elsevier (2003).
  2. 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]
  3. S. Bartels, X. Fenga and A. Prohl, Finite element approximations of wave maps into spheres. SIAM J. Numer. Anal. 46 (2007) 61–87. [CrossRef] [MathSciNet]
  4. A. Bossavit, Mixed finite elements and the complex of Whitney forms, in The mathematics of finite elements and applications VI, J. Whiteman Ed., Academic Press, London (1988) 137–144.
  5. J.H. Bramble, J.E. Pasciak and O. Steinbach, On the stability of the L2 projection in H1(Ω). Math. Comput. 71 (2001) 147–156. [CrossRef] [MathSciNet]
  6. S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods. Second edition, Springer (2002).
  7. S.H. Christiansen, Résolution des équations intégrales pour la diffraction d'ondes accoustiques et électromagnétiques. Ph.D. thesis, École polytechnique, France (2002).
  8. S.H. Christiansen, Discrete Fredholm properties and convergence estimates for the Electric Field Integral Equation. Math. Comput. 73 (2004) 143–167.
  9. S.H. Christiansen, Constraint preserving schemes for gauge invariant wave equations. SIAM J. Sci. Comput. 31 (2009) 1448–1469. [CrossRef]
  10. S.H. Christiansen and R. Winther, On constraint preservation in numerical simulations of Yang-Mills equations. SIAM J. Sci. Comput. 28 (2006) 75–101. [CrossRef] [MathSciNet]
  11. S.H. Christiansen and R. Winther, Smoothed projections in finite element exterior calculus. Math. Comput. 77 (2007) 813–829. [CrossRef]
  12. P.G. Ciarlet, Basic error estimates for elliptic problems, in Handbook of numerical analysis II, P.G. Ciarlet and J.-L. Lions Eds., North Holland (1991) 17–351.
  13. M. Crouzeix and V. Thomée, The stability in Lp and W1p of the L2-projection onto finite element function spaces. Math. Comput. 48 (1987) 521–532.
  14. J. Douglas Jr., T. Dupont and L. Wahlbin, The stability in Lq of the L2-projection into finite element function spaces. Numer. Math. 23 (1975) 193–197. [CrossRef]
  15. F. Dubois, Discrete vector potential representation of a divergence free vector field in three-dimensional domains: Numerical analysis of a model problem. SIAM J. Numer. Anal. 27 (1990) 1103–1141. [CrossRef] [MathSciNet]
  16. J. Ginibre and G. Velo, The Cauchy problem for coupled Yang-Mills and scalar fields in the temporal gauge. Commun. Math. Phys. 82 (1981) 1–28. [CrossRef]
  17. V. Girault and P.-A. Raviart, Finite Element approximation of the Navier-Stokes equations. Springer-Verlag, Berlin (1986).
  18. F. Kikuchi, On a discrete compactness property for the Nédélec finite elements. J. Fac. Sci. Univ. Tokyo, Sect. 1A Math. 36 (1989) 479–490.
  19. S. Klainerman, Mathematical challenges of general relativity. Rend. Mat. Appl. 27 (2007) 105–122. [MathSciNet]
  20. S. Klainerman and M. Machedon, On the Maxwell-Klein-Gordon equation with finite energy. Duke Math. J. 74 (1994) 19–44. [CrossRef] [MathSciNet]
  21. S. Klainerman and M. Machedon, Finite energy solutions of the Yang-Mills equations in R3+1. Ann. Math. 142 (1995) 39–119. [CrossRef]
  22. E.H. Lieb and M. Loss, Analysis Graduate Studies in Mathematics 14. Second edition, AMS (2001).
  23. J.L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications 1. Dunod, Paris (1968).
  24. N. Masmoudi and K. Nakanishi, Uniqueness of Finite Energy solutions for Maxwell-Dirac and Maxwell-Klein-Gordon equations. Commun. Math. Phys. 243 (2003) 123–136. [CrossRef]
  25. P. Monk, Finite Element Methods for Maxwell's Equations. Oxford Science Publication (2003).
  26. J. Schöberl, A posteriori error estimates for Maxwell equations. Math. Comput. 77 (2008) 633–649.
  27. S. Selberg and A. Tesfahun, Finite-energy global well-posedness of the Maxwell-Klein-Gordon system in Lorenz gauge. Commun. Partial Differ. Equ. 35 (2010) 1029–1057. [CrossRef]
  28. J. Shatah and M. Struwe, Geometric wave equations, Courant Lecture Notes in Mathematics 2. New York University, Courant Institute of Mathematical Sciences, New York, American Mathematical Society, Providence (1998).
  29. C.G. Simader, On Dirichlet Boundary Value Problem. Springer-Verlag (1972).
  30. J. Simon, Compact sets in the space Lp(0,T;B). Ann. Mat. Pura. Appl. 146 (1987) 65–96.
  31. T. Tao, Local well-posedness of the Yang-Mills equation in the temporal gauge below the energy norm. J. Differ. Equ. 189 (2003) 366–382. [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