Geodesic
Convergence of a discrete scheme in a regularization method for the quasi-stationary Maxwell system in a non-homogeneous conducting medium
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 3, pp. 319-332 
M. V. Urev. Convergence of a discrete scheme in a regularization method for the quasi-stationary Maxwell system in a non-homogeneous conducting medium. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 3, pp. 319-332. http://geodesic.mathdoc.fr/item/SJVM_2011_14_3_a7/
@article{SJVM_2011_14_3_a7,
     author = {M. V. Urev},
     title = {Convergence of a~discrete scheme in a~regularization method for the quasi-stationary {Maxwell} system in a~non-homogeneous conducting medium},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {319--332},
     year = {2011},
     volume = {14},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2011_14_3_a7/}
}
TY  - JOUR
AU  - M. V. Urev
TI  - Convergence of a discrete scheme in a regularization method for the quasi-stationary Maxwell system in a non-homogeneous conducting medium
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2011
SP  - 319
EP  - 332
VL  - 14
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SJVM_2011_14_3_a7/
LA  - ru
ID  - SJVM_2011_14_3_a7
ER  - 
%0 Journal Article
%A M. V. Urev
%T Convergence of a discrete scheme in a regularization method for the quasi-stationary Maxwell system in a non-homogeneous conducting medium
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2011
%P 319-332
%V 14
%N 3
%U http://geodesic.mathdoc.fr/item/SJVM_2011_14_3_a7/
%G ru
%F SJVM_2011_14_3_a7

Voir la notice de l'article provenant de la source Math-Net.Ru

Convergence of a discrete solution to the solution of a regularized system of the Maxwell equations written in terms of a vector magnetic potential with a special calibration of the medium conductance is considered. The problem is discretized by the Nedelec vector finite element method in space and by the implicit Euler scheme in time. An optimal theoretical energy estimate of the approximate solution error in the 3D Lipschitz polyhedral domains is obtained.

[1] Kalinin A. V., Kalinkina A. A., “Kvazistatsionarnye nachalno-kraevye zadachi dlya sistemy uravnenii Maksvella”, Vestnik NNGU. Matematicheskoe modelirovanie i optimalnoe upravlenie (Nizhnii Novgorod), 2003, no. 26, 21–39

[2] Gudovich I. S., Krein S. G., Kulikov I. M., “Kraevye zadachi dlya uravnenii Maksvella”, Doklady AN SSSR, 207:2 (1972), 321–324 | MR

[3] Ivanov M. I., Kateshov V. A., Kremer I. A., Urev M. V., “Reshenie trekhmernykh nestatsionarnykh zadach impulsnoi elektrorazvedki”, Avtometriya, 43:2 (2007), 33–44

[4] Kremer I. A., Urev M. V., “Metod regulyarizatsii statsionarnoi sistemy Maksvella v neodnorodnoi provodyaschei srede”, Sib. zhurn. vychisl. matematiki (Novosibirsk), 12:2 (2009), 161–170 | Zbl

[5] Kremer I. A., Urev M. V., “Reshenie metodom konechnykh elementov regulyarizirovannoi zadachi dlya statsionarnogo magnitnogo polya v neodnorodnoi provodyaschei srede”, Sib. zhurn. vychisl. matematiki (Novosibirsk), 13:1 (2010), 33–49 | Zbl

[6] Kremer I. A., Urev M. V., “Metod regulyarizatsii dlya kvazistatsionarnoi sistemy Maksvella v neodnorodnoi provodyaschei srede”, Vestnik NGU. Seriya: Matematika, mekhanika, informatika, 11:1 (2011), 35–44

[7] Nedelec J. C., “A new family of mixed finite elements in $\mathbb R^3$”, Numer. Math., 50 (1986), 57–81 | DOI | MR | Zbl

[8] Syarle F., Metod konechnykh elementov dlya ellipticheskikh zadach, Mir, M., 1980 | MR

[9] Girault V., Raviart P.-A., Finite Element Methods for Navier–Stokes Equations, Springer-Verlag, Berlin, 1986 | MR | Zbl

[10] Amrouche C., Bernardi C., Dauge M., Girault V., “Vector potentials in three-dimensional nonsmooth domains”, Math. Meth. Appl. Sci., 21:9 (1998), 823–864 | 3.0.CO;2-B class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[11] Costabel M., Dauge M., Nicaise S., “Singularities of Maxwell interface problems”, M2AN Math. Model. Numer. Anal., 33:3 (1999), 627–649 | DOI | MR | Zbl

[12] Ciarlet P., Zou J., “Fully discrete finite element approaches for time-dependent Maxwell's equations”, Numer. Math., 82 (1999), 193–219 | DOI | MR | Zbl

[13] Chen Z., Du Q., Zou J., “Finite element methods with matching and non-matching meshes for Maxwell equations with discontinuous coefficients”, SIAM J. Numer. Anal., 37 (2000), 1542–1570 | DOI | MR | Zbl

[14] Alonso A., Valli A., “An optimal domain decomposition preconditioner for low-frequency time-harmonic Maxwell equations”, Math. Comp., 68:226 (1999), 607–631 | DOI | MR | Zbl

[15] Lions Zh.-L., Madzhenes E., Neodnorodnye granichnye zadachi i ikh prilozheniya, Mir, M., 1971 | Zbl

[16] Dyuvo G., Lions Zh.-L., Neravenstva v mekhanike i fizike, Nauka, M., 1980 | MR