Free Access
Issue
ESAIM: M2AN
Volume 50, Number 5, September-October 2016
Page(s) 1457 - 1489
DOI https://doi.org/10.1051/m2an/2015086
Published online 08 September 2016
  1. R. A. Adams and J.J. Fournier, Sobolev spaces, 2nd edition. Vol. 140 of Pure and Applied Mathematics. Academic Press, New York, NY (2003) 305. [Google Scholar]
  2. D.N. Arnold, R.S. Falk and R. Winther, Finite element exterior calculus: from Hodge theory to numerical stability. Bull. Amer. Math. Soc. (N.S.) 47 (2010) 281–354. [CrossRef] [MathSciNet] [Google Scholar]
  3. I. Babuška and J. Osborn, Eigenvalue problems. In Finite Element Methods (Part 1). Vol. 2 of Handbook of Numerical Analysis. Elsevier (1991) 641–787. [Google Scholar]
  4. S. Badia and R. Codina, A nodal-based finite element approximation of the Maxwell problem suitable for singular solutions. SIAM J. Numer. Anal. 50 (2012) 398–417. [CrossRef] [MathSciNet] [Google Scholar]
  5. A. Bonito and J.-L. Guermond, Approximation of the eigenvalue problem for the time harmonic Maxwell system by continuous Lagrange finite elements. Math. Comput. 80 (2011) 1887–1910. [CrossRef] [Google Scholar]
  6. A. Bonito, J.-L. Guermond and F. Luddens, Regularity of the Maxwell equations in heterogeneous media and Lipschitz domains. J. Math. Anal. Appl. 408 (2013) 498–512. [CrossRef] [MathSciNet] [Google Scholar]
  7. J. Bramble and J. Pasciak, A new approximation technique for div-curl systems. Math. Comput. 73 (2004) 1739–1762 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  8. J. Bramble, T. Kolev and J. Pasciak, The approximation of the Maxwell eigenvalue problem using a least-squares method. Math. Comput. 74 (2005) 1575–1598 (electronic). [CrossRef] [Google Scholar]
  9. A. Buffa and P. Ciarlet Jr., On traces for functional spaces related to Maxwell’s equations. I. An integration by parts formula in Lipschitz polyhedra. Math. Methods Appl. Sci. 24 (2001) 9–30. [CrossRef] [MathSciNet] [Google Scholar]
  10. A. Buffa, P. Ciarlet Jr and E. Jamelot, Solving electromagnetic eigenvalue problems in polyhedral domains with nodal finite elements. Numer. Math. 113 (2009) 497–518. [CrossRef] [MathSciNet] [Google Scholar]
  11. A. Buffa, P. Houston and I. Perugia, Discontinuous Galerkin computation of the Maxwell eigenvalues on simplicial meshes. J. Comput. Appl. Math. 204 (2007) 317–333. [CrossRef] [MathSciNet] [Google Scholar]
  12. A. Buffa and I. Perugia, Discontinuous Galerkin approximation of the Maxwell eigenproblem. SIAM J. Numer. Anal. 44 (2006) 2198–2226 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  13. S.H. Christiansen and R. Winther, Smoothed projections in finite element exterior calculus. Math. Comput. 77 (2008) 813–829. [CrossRef] [Google Scholar]
  14. R. Clough and J. Tocher, Finite element stiffness matrices for analysis of plates in bending. In Conf. on Matrix Methods in Structural Mechanics. Wright-Patterson A.F.B. (1965) 515–545. [Google Scholar]
  15. M. Costabel, A coercive bilinear form for Maxwell’s equations. J. Math. Anal. Appl. 157 (1991) 527–541. [CrossRef] [MathSciNet] [Google Scholar]
  16. M. Costabel and M. Dauge, Weighted Regularization of Maxwell Equations in Polyhedral Domains. Numer. Math. 93 (2002) 239–278. [CrossRef] [MathSciNet] [Google Scholar]
  17. M. Dauge, Benchmark for Maxwell (2009). Available at http://perso.univ-rennes1.fr/monique.dauge/benchmax.html. [Google Scholar]
  18. H. Duan, P. Lin and R.C.E. Tan, C0 elements for generalized indefinite Maxwell equations. Numer. Math. 122 (2012) 61–99. [CrossRef] [MathSciNet] [Google Scholar]
  19. H.-Y. Duan, F. Jia, P. Lin and R.C.E. Tan, The local L2 projected C0 finite element method for Maxwell problem. SIAM J. Numer. Anal. 47 (2009) 1274–1303. [CrossRef] [MathSciNet] [Google Scholar]
  20. A. Giesecke, C. Nore, F. Stefani, G. Gerbeth, J. Léorat, W. Herreman, F. Luddens and J.-L. Guermond, Influence of high-permeability discs in an axisymmetric model of the cadarache dynamo experiment. New J. Phys. 14 (2012). [Google Scholar]
  21. A. Giesecke, C. Nore, F. Stefani, G. Gerbeth, J. Léorat, F. Luddens and J.-L. Guermond, Electromagnetic induction in non-uniform domains. Geophys. Astrophys. Fluid Dyn. 104 (2010) 505–529. [CrossRef] [MathSciNet] [Google Scholar]
  22. P. Grisvard, Elliptic problems in nonsmooth domains. Vol. 24 of Monographs and Studies in Mathematics. Pitman, Advanced Publishing Program, Boston, MA (1985). [Google Scholar]
  23. J.-L. Guermond, The LBB condition in fractional Sobolev spaces and applications. IMA J. Numer. Anal. 29 (2009) 790–805. [CrossRef] [MathSciNet] [Google Scholar]
  24. J.-L. Guermond, J. Léorat, F. Luddens, C. Nore and A. Ribeiro, Effects of discontinuous magnetic permeability on magnetodynamic problems. J. Comput. Phys. 230 (2011) 6299–6319. [CrossRef] [MathSciNet] [Google Scholar]
  25. W. Herreman, C. Nore, L. Cappanera and J.-L. Guermond, Tayler instability in liquid metal columns and liquid metal batteries. J. Fluid Mech. 771 (2015) 79–114. [CrossRef] [MathSciNet] [Google Scholar]
  26. S. Hofmann, M. Mitrea and M. Taylor, Geometric and transformational properties of Lipschitz domains, Semmes–Kenig–Toro domains, and other classes of finite perimeter domains. J. Geom. Anal. 17 (2007) 593–647. [CrossRef] [MathSciNet] [Google Scholar]
  27. R. Hollerbach, C. Nore, P. Marti, S. Vantieghem, F. Luddens and J. Léorat, Parity-breaking flows in precessing spherical containers. Phys. Rev. E 87 (2013). [CrossRef] [Google Scholar]
  28. R. Lehoucq, D. Sorensen and C. Yang, ARPACK users’ guide. Solution of large-scale eigenvalue problems with implictly restarted Arnoldi methods. Vol. 6 of Software, Environments and Tools. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1998. [Google Scholar]
  29. J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Vol. 1. Dunod, Paris, France (1968). [Google Scholar]
  30. F. Luddens, Analyse théorique et numérique des équations de la magnétohydrodynamique: applications à l’effet dynamo. Ph.D. thesis, December 6 (2012). [Google Scholar]
  31. R. Monchaux, M. Berhanu, M. Bourgoin, P. Odier, M. Moulin, J.-F. Pinton, R. Volk, S. Fauve, N. Mordant, F. Pétrélis, A. Chiffaudel, F. Daviaud, B. Dubrulle, C. Gasquet, L. Marié and F. Ravelet, Generation of magnetic field by a turbulent flow of liquid sodium. Phys. Rev. Lett. 98 (2007) 044502. [NASA ADS] [CrossRef] [PubMed] [Google Scholar]
  32. P. Monk, Finite element methods for Maxwell’s equations. Numerical Mathematics and Scientific Computation. Oxford University Press, New York (2003). [Google Scholar]
  33. J. Osborn, Spectral Approximation for Compact Operators. Math. Comput. 29 (1975) 712–725. [Google Scholar]
  34. M.J.D. Powell and M.A. Sabin, Piecewise quadratic approximations on triangles. ACM Trans. Math. Software 3 (1977) 316–325. [CrossRef] [MathSciNet] [Google Scholar]
  35. J. Schöberl, A posteriori error estimates for Maxwell equations. Math. Comput. 77 (2008) 633–649. [Google Scholar]
  36. L. Tartar, An introduction to Sobolev spaces and interpolation spaces. Vol. 3 of Lect. Notes Unione Mat. Italiana. Springer, Berlin (2007). [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