Time-discrete finite element schemes for Maxwell's equations
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 29 (1995) no. 2, p. 171-197
@article{M2AN_1995__29_2_171_0,
     author = {Makridakis, Ch. G. and Monk, P.},
     title = {Time-discrete finite element schemes for Maxwell's equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {29},
     number = {2},
     year = {1995},
     pages = {171-197},
     zbl = {0834.65120},
     mrnumber = {1332480},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1995__29_2_171_0}
}
Makridakis, Ch. G.; Monk, P. Time-discrete finite element schemes for Maxwell's equations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 29 (1995) no. 2, pp. 171-197. http://www.numdam.org/item/M2AN_1995__29_2_171_0/

[1] J. Adam, A. Servenière, J. Nédélec and P. Raviart, 1980, Study of an implicit scheme for integrating Maxwell's equations, Comp.Meth. Appl. Mech. Eng., 22, 327-346. | MR 579675 | Zbl 0433.73067

[2] G. Baker and J. Bramble, 1979, Semidiscrete and single step fully discrete approximations for second order hyperbolic equations, RAIRO Anal. Numer, 13, 75-100. | Numdam | MR 533876 | Zbl 0405.65057

[3] A. Bossavit, 1990, Solving Maxwell equations in a closed cavity, and the question of « spurious » modes, IEEE Trans. Mag., 26, 702-705.

[4] P. Ciarlet, 1978, The Finite Element Method for Elliptic Problems, vol. 4 of Studies in Mathematics and It's Applications, Elsevier North-Holland, NewYork. | MR 520174 | Zbl 0383.65058

[5] F. Dubois, 1990, 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, 1103-1142. | MR 1061122 | Zbl 0717.65086

[6] V. Glrault, 1988, Incompressible finite element methods for Navier-Stokes equations with nonstandard boundary conditions in R3, Math. Comp., 51,53-58. | Zbl 0666.76053

[7] V. Girault, 1990, Curl-conforming finite element methods for Navier-Stokes equations with non-standard boundary conditions in R3, in The Navier-Stokes equations. Theory and Numerical Methods, Lecture Notes, 1431,Springer, 201-218. | MR 1072191 | Zbl 0702.76037

[8] V. Girault and P. Raviart, 1986, Finite Element Methods for Navier-Stokes Equations, Springer-Verlag, New York. | MR 851383 | Zbl 0585.65077

[9] M. Křížek and P. Neittaanmäki, 1989, On time-harmonic Maxwell equations with nonhomogeneous conductivities : solvability and FE-approximation, Aplikace Matematiky, 34, 480-499. | MR 1026513 | Zbl 0696.65085

[10] R. Leis, 1988, Initial Boundary Value Problems in Mathematical Physics, John Wiley, New York. | Zbl 0599.35001

[11] K. Mahadevan and R. Mittra, 1993, Radar cross section computations of inhomogeneous scatterers using edge-based finite element method in frequency and time domains, Radio Science, 28, 1181-1193.

[12] K. Mahadevan, R. Mittra and P. M. Vaidya, 1993, Use of Whitney's edge and face elements for efficient finite element time domain solution of Maxwell's equation, Preprint.

[13] C. G. Makridakis, 1992, On mixed finite element methods in linear elastodynamics, Numer. Math., 61, 235-260. | MR 1147578 | Zbl 0734.73074

[14] P. Monk, 1993, An analysis of Nédélec's method for the spatial discretization of Maxwell's equations, J. Comp. Appl. Math., 47, 101-121. 3 | MR 1226366 | Zbl 0784.65091

[15] J. Nédélec, 1980, Mixed finite elements in R3, Numer. Math., 35, 315-341. | MR 592160 | Zbl 0419.65069

[16] J. Nédélec, Éléments finis mixtes incompressibles pour l'équation de Stokes dans R3, Numer. Math., 39, 97-112. | Zbl 0488.76038

[17] K. Yee, 1966, Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media, IEEE Trans. on Antennas and Propagation, AP-16, 302-307. | Zbl 1155.78304