References
- F. Assous, P. Ciarlet Jr. and S. Labrunie. Theoretical tools to solve the axisymmetric maxwell equations. Math. Meth. Appl. Sci., 25:49–78, 2002. http://dx.doi.org/10.1002/mma.279.
- F. Assous, P. Ciarlet Jr. and S. Labrunie. Solution of axisymmetric maxwell equations. Math. Meth. Appl. Sci., 26:861–896, 2003. http://dx.doi.org/10.1002/mma.400.
- F. Assous, P. Ciarlet Jr. and J. Segré. Numerical solution to the time-dependent Maxwell equations in two-dimensional singular domain: The singular complement method. J. Comput. Phys., 161:218–249, 2000. http://dx.doi.org/10.1006/jcph.2000.6499.
- R. Becker, P. Hansbo and R. Stenberg. A finite element method for domain decomposition with non-matching grids. M2AN, 37:209–225, 2003.
- M.Sh. Birman and M.Z. Solomyak. L2-theory of the Maxwell operator in arbitrary domains. Russian Math. Surveys, 42:75–96, 1987. http://dx.doi.org/10.1070/RM1987v042n06ABEH001505.
- M.Sh. Birman and M.Z. Solomyak. The weyl asymptotic decomposition of the spectrum of the Maxwell operator for domain with lipschitzian boundary. Vestnik. Leningr. Univ. Math., 20:15–21, 1987.
- J. Van Bladel. Electromagnetic Fields. McGraw-Hill, New York, 1985.
- M. Cessenat. Mathematical Methods in Electromagnetism. Linear Theory and Applications, volume 41 of Advances in Mathematics for Applied Sciences. World Scientific, Singapore, 1996.
- G. Cohen. Higher Order Numerical Methods for Transient Wave Equations. Springer, New York, 2002.
- D.M Copeland, J. Gopalakrishnan and J.E. Pasciak. A mixed method for axisymmetric div–curl systems. Math. Comput., 77(264):1941–1965, 2008. http://dx.doi.org/10.1090/S0025-5718-08-02102-9.
- M. Costabel. A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains. Math. Meth. Appl. Sci., 12:365–368, 1990. http://dx.doi.org/10.1002/mma.1670120406.
- M. Costabel and M. Dauge. Maxwell and Lamé eigenvalues on polyhedral domains. Math. Meth. Appl. Sci., 22:243–258, 1999.
- M. Costabel and M. Dauge. Weighted regularization of maxwell equations in polyhedral domains. Numer. Math., 93:239–277, 2002. http://dx.doi.org/10.1007/s002110100388.
- A.-S. Bonnet-Ben Dhia, C. Hazard and S. Lohrengel. A singular field method for the solution of Maxwell's equations in polyhedral domains. SIAM J. Appl. Math., 59:2028–2044, 1999. http://dx.doi.org/10.1137/S0036139997323383.
- P. Grisvard. Elliptic Problems in Nonsmooth Domains, volume 24 of Monogr. Stud. Math. Pitman, London, 1985.
- P. Grisvard. Singularities in Boundary Value Problems, volume 22 of RMA. Masson, Paris, 1992.
- C. Hazard. Numerical simulation of corner singularities: a paradox in maxwell like problems. C. R. Acad. Sci. Paris, Ser. IIb, 330:57–68, 2002.
- Frédéric Hecht. FreeFem ++. Laboratoire J.L. Lions, Universit′e Pierre et Marie Curie, 2010.
- J.D. Jackson. Classical Electrodynamics. John Wiley and Sons, New York, 1975.
- E. Jamelot. A nodal finite element method for Maxwell's equations. C. R. Acad. Sci. Paris, Ser. I, 339:809–814, 2004.
- V.A. Kondrat'ev. The smoothness of solutions of Dirichlet's problem for second order elliptic equation in a region with a piecewise-smooth boundary. Differential Equations, 6:1392–1401, 1976.
- V.A. Kondrat'ev. Singularities of a solution of Dirichlet's problem for a second-order equation in the neighborhood of an edge. Differential Equations, 13:1411–1415, 1977.
- H. Li. Finite element analysis for the axisymmetric laplace operator on polygonal domains. J. Comput. Appl. Math., 235:5155–5176, 2011. http://dx.doi.org/10.1016/j.cam.2011.05.003.
- P. Monk. Finite element methods for Maxwell's equations. Oxford University Press, 2003.
- J. Nitsche. Über ein Variationsprinzip zur losung von Dirichlet-Problemen bei Verwendung von Teilrumen, die keinen Randbedingungen unterworfen sind. Abh. Math, Sem. Univ. Hamburg, 36:9–15, 1971. http://dx.doi.org/10.1007/BF02995904.
- R. Stenberg. On some techniques for approximating boundary conditions in the finite element method. J. Comput. Appl. Math., 63:139–148, 1995. http://dx.doi.org/10.1016/0377-0427(95)00057-7.