Geodesic
Convergence of the Galerkin methods for equations with elliptic operators on subspaces and solving the electric field equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 1, pp. 129-139 Cet article a éte moissonné depuis la source Math-Net.Ru

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Application of the Galerkin methods to the numerical analysis of the integro-differential electric field equation is justified. The convergence of the Galerkin methods is established for a class of equations with nonelliptic operators comprising the electric field equation. Theorems concerning the approximation of the elements belonging to a special Sobolev space by the basis Rao–Wilton–Glisson functions are proved. The rate of convergence is estimated. 
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Yu. G. Smirnov. Convergence of the Galerkin methods for equations with elliptic operators on subspaces and solving the electric field equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 1, pp. 129-139. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_1_a12/

[1] Maue A. W., “Toward formulator of a general diffraction problem via an integral equation”, Z. Phys., 126 (1949), 601–618 | DOI | MR | Zbl

[2] Khenl X., Maue A., Vestpfal K., Teoriya difraktsii, Mir, M., 1964

[3] Smirnov Yu. G., “O fredgolmovosti zadachi difraktsii na ploskom ogranichennom idealno provodyaschem ekrane”, Dokl. AN SSSR, 319:1 (1991), 147–149

[4] Smirnov Yu. G., “O fredgolmovosti sistemy psevdodifferentsialnykh uravnenii v zadache difraktsii na ogranichennom ekrane”, Differents. ur-niya, 28:1 (1992), 136–143

[5] Smirnov Yu. G., “O razreshimosti vektornykh integrodifferentsialnykh uravnenii v zadache difraktsii elektromagnitnogo polya na ekranakh proizvolnoi formy”, Zh. vychisl. matem. i matem. fiz., 34:10 (1994), 1461–1475 | MR | Zbl

[6] Ilinskii A. C., Smirnov Yu. G., Difraktsiya elektromagnitnykh voln na provodyaschikh tonkikh ekranakh, IPRZhR, M., 1996

[7] Ilyinsky A. S., Smirnov Yu. G., Electromagnetic wave diffraction by conducting screens, VSP, Utrecht, 1998

[8] Harrington R. F., Field Computation by moment methods, Macmillian Co., New York, 1968

[9] R. Mittra (red.), Vychislitelnye metody v elektrodinamike, Mir, M., 1977 | MR

[10] E. K. Miller, L. Medgyesi-Mitschand, E. H. Newman (ed.), Computational electromagnetics: Frequency-domain method of moments, IEEE Press, New York, 1992

[11] Kress R., Linear integral equations, Appl. Mathem. Sci., 8, Springer, New York, 1989 | MR

[12] Costabel M., “Boundary integral operators on Lipschitz domains: Elementary results”, SIAM J. Math. Analys., 19:3 (1988), 613–626 | DOI | MR | Zbl

[13] Tribel X., Teoriya interpolyatsii, funktsionalnye prostranstva, differentsialnye operatory, Mir, M., 1980 | MR

[14] Novikov S. P., Fomenko A. T., Elementy differentsialnoi geometrii i topologii, Nauka, M., 1987 | MR

[15] Rao S. M., Wilton D. R., Glisson A. W., “Electromagnetic scattering by surfaces of arbitrary shape”, IEEE Trans. Antennas Propagation, AP-30:3 (1982), 409–418 | DOI

[16] Raviart P. A., Thomas J.-M., “A mixed finite element method for 2nd order elliptic problems”, Lect. Notes in Math., 606, Springer, Berlin, New York, 1977, 292–315 | MR

[17] Nedelec J.-C., “Mixed finite elements in $R^3$”, Numer. Math., 35 (1980), 315–341 | DOI | MR | Zbl