Free Access
Issue |
ESAIM: M2AN
Volume 45, Number 4, July-August 2011
|
|
---|---|---|
Page(s) | 739 - 760 | |
DOI | https://doi.org/10.1051/m2an/2010100 | |
Published online | 21 February 2011 |
- R.A Adams and J.J.F. Fournier, Sobolev Spaces – Pure and Applied Mathematics Series. Second edition, Elsevier (2003). [Google Scholar]
- 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]
- S. Bartels, X. Fenga and A. Prohl, Finite element approximations of wave maps into spheres. SIAM J. Numer. Anal. 46 (2007) 61–87. [Google Scholar]
- 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. [Google Scholar]
- 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. [Google Scholar]
- S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods. Second edition, Springer (2002). [Google Scholar]
- S.H. Christiansen, Résolution des équations intégrales pour la diffraction d'ondes accoustiques et électromagnétiques. Ph.D. thesis, École polytechnique, France (2002). [Google Scholar]
- S.H. Christiansen, Discrete Fredholm properties and convergence estimates for the Electric Field Integral Equation. Math. Comput. 73 (2004) 143–167. [Google Scholar]
- S.H. Christiansen, Constraint preserving schemes for gauge invariant wave equations. SIAM J. Sci. Comput. 31 (2009) 1448–1469. [CrossRef] [Google Scholar]
- 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] [Google Scholar]
- S.H. Christiansen and R. Winther, Smoothed projections in finite element exterior calculus. Math. Comput. 77 (2007) 813–829. [Google Scholar]
- 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. [Google Scholar]
- 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. [Google Scholar]
- 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] [Google Scholar]
- 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] [Google Scholar]
- 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] [Google Scholar]
- V. Girault and P.-A. Raviart, Finite Element approximation of the Navier-Stokes equations. Springer-Verlag, Berlin (1986). [Google Scholar]
- F. Kikuchi, On a discrete compactness property for the Nédélec finite elements. J. Fac. Sci. Univ. Tokyo, Sect. 1A Math. 36 (1989) 479–490. [Google Scholar]
- S. Klainerman, Mathematical challenges of general relativity. Rend. Mat. Appl. 27 (2007) 105–122. [MathSciNet] [Google Scholar]
- S. Klainerman and M. Machedon, On the Maxwell-Klein-Gordon equation with finite energy. Duke Math. J. 74 (1994) 19–44. [CrossRef] [MathSciNet] [Google Scholar]
- S. Klainerman and M. Machedon, Finite energy solutions of the Yang-Mills equations in R3+1. Ann. Math. 142 (1995) 39–119. [CrossRef] [Google Scholar]
- E.H. Lieb and M. Loss, Analysis Graduate Studies in Mathematics 14. Second edition, AMS (2001). [Google Scholar]
- J.L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications 1. Dunod, Paris (1968). [Google Scholar]
- 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] [Google Scholar]
- P. Monk, Finite Element Methods for Maxwell's Equations. Oxford Science Publication (2003). [Google Scholar]
- J. Schöberl, A posteriori error estimates for Maxwell equations. Math. Comput. 77 (2008) 633–649. [Google Scholar]
- 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] [Google Scholar]
- 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). [Google Scholar]
- C.G. Simader, On Dirichlet Boundary Value Problem. Springer-Verlag (1972). [Google Scholar]
- J. Simon, Compact sets in the space Lp(0,T;B). Ann. Mat. Pura. Appl. 146 (1987) 65–96. [Google Scholar]
- 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] [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.