no. 2
Finite element convergence for the Darwin model to Maxwell's equations
ESAIM: Modélisation mathématique et analyse numérique, Tome 31 (1997) no. 2, pp. 213-249. 
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     author = {Ciarlet, P. Jr. and Zou, Jun},
     title = {Finite element convergence for the {Darwin} model to {Maxwell's} equations},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {213--249},
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     volume = {31},
     number = {2},
     year = {1997},
     mrnumber = {1437121},
     zbl = {0887.65121},
     language = {en},
     url = {http://archive.numdam.org/item/M2AN_1997__31_2_213_0/}
}
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Ciarlet, P. Jr.; Zou, Jun. Finite element convergence for the Darwin model to Maxwell's equations. ESAIM: Modélisation mathématique et analyse numérique, Tome 31 (1997) no. 2, pp. 213-249. http://archive.numdam.org/item/M2AN_1997__31_2_213_0/

[1] R. A. Adams, 1975, Sobolev spaces. Academic Press, New York, 1975. | MR | Zbl

[2] J. J. Ambrosiano, S. T. Brandon and E. Sonnendrucker, 1995, A finite element formulation of the Darwin PIC model for use on unstructured grids J. Comput. Physics, 121(2), 281-297. | MR | Zbl

[3] I. Babuska, 1973, The finite element method with Lagrange multipliers Numer. Math, 20, 179-192. | MR | Zbl

[4] M. Bercovier and O. Pironneau, 1979, Error estimates for the finite element method solution of the Stokes problem in the primitive variables Numer. Math., 33, 211-224. | MR | Zbl

[5] F. Brezzi, 1974, On the existence, uniqueness and approximation of saddle point problems arising from Lagrange multipliers. RAIRO Anal. Numer., 129-151. | Numdam | MR | Zbl

[6] F. Brezzi and M. Fortin, 1991, Mixed and hybrid finite element methods. Springer-Verlag, Berlin. | MR | Zbl

[7] P. Ciarlet, 1978, The finite element method for elliptic problems. North-Holland, Amsterdam. | MR | Zbl

[8] P. Degond and P. A. Raviart, 1992, An analysis of the Darwin model of approximation to Maxwell's equations Forum Math., 4, 13-44. | MR | Zbl

[9] V. Girault and P.-A. Raviart, 1986, Finite element methods for Navier-Stokes equations. Springer-Verlag, Berlin. | MR | Zbl

[10] P. Grisvard, 1985, Elliptic problems in nonsmooth domains. Pitman, Advanced Pubhshing Program, Boston. | MR | Zbl

[11] D. W. Hewett and J. K. Boyd, 1987, Streamlined Darwin simulation of nonneutral plasmas. J. Comput. Phys., 73, 166-181. | MR | Zbl

[12] D. W. Hewett and C. Nielson, 1978, A multidimensional quasineutral plasma simulation model. J. Comput. Phys. 29, 219-236. | Zbl

[13] P. Hood and G. Taylor, 1974, Navier-Stokes equation using mixed interpolation. In Oden, editor, Finite element methods in flow problems. UAH Press.

[14] J.-L. Lions and E. Magenes, 1968, Problèmes aux limites non homogènes et applications. Dunod, Paris. | Zbl

[15] J.-C. Nedelec, 1980, Mixed finite éléments in R3. Numer. Math., 35, 315-341. | MR | Zbl

[16] J.-C. Nedelec, 1982, Eléments finis mixtes incompressibles pour l'équation de Stokes dans R3. Numer. Math., 39, 97-112. | MR | Zbl

[17] C. Nlelson and H. R. Lewis, 1976, Particle code models in the non radiative limit. Methods Comput. Phys., 16, 367-388.

[18] P.-A. Raviart, 1993, Finite element approximation of the time-dependent Maxwell equations. Technical report, Ecole Polytechnique, France, GdR SPARCH #6.

[19] R. Verfurth, 1984, Error estimates for a mixed finite element approximation of the Stokes equations. RAIRO Anal. Numer., 18(2), 175-182. | Numdam | MR | Zbl

[20] C. Weber, 1980, A local compactness theorem for Maxwell's equations. Math. Meth. in the Appl. Sci., 2, 12-25. | MR | Zbl