Geodesic
The convergence of finite element method for axially symmetric magnetostatic problem
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 9 (2006) no. 1, pp. 63-79 
M. V. Urev. The convergence of finite element method for axially symmetric magnetostatic problem. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 9 (2006) no. 1, pp. 63-79. http://geodesic.mathdoc.fr/item/SJVM_2006_9_1_a6/
@article{SJVM_2006_9_1_a6,
     author = {M. V. Urev},
     title = {The convergence of finite element method for axially symmetric magnetostatic problem},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {63--79},
     year = {2006},
     volume = {9},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2006_9_1_a6/}
}
TY  - JOUR
AU  - M. V. Urev
TI  - The convergence of finite element method for axially symmetric magnetostatic problem
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2006
SP  - 63
EP  - 79
VL  - 9
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SJVM_2006_9_1_a6/
LA  - ru
ID  - SJVM_2006_9_1_a6
ER  - 
%0 Journal Article
%A M. V. Urev
%T The convergence of finite element method for axially symmetric magnetostatic problem
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2006
%P 63-79
%V 9
%N 1
%U http://geodesic.mathdoc.fr/item/SJVM_2006_9_1_a6/
%G ru
%F SJVM_2006_9_1_a6

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

This paper considers a problem of calculation of stationary magnetic linear axially symmetric fields in non-homogeneous media. As distinct from conventional formulations of this problem in terms of the azimuthal vector potential component or a function of a magnetic field flow, the present paper offers the reduction to another sought for function satisfying the equation to be most convenient for investigation. The principal feature of the problem formulated is in its degeneracy on the axis of symmetry demanding the corresponding spaces with a weight when studying the problem. For the finite element method with piecewise linear elements, the convergence of an approximate solution to the exact one is proved with an error estimation not worse than in the case of the elliptic equation without degeneracy.

[1] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1964 | MR

[2] Assous F., Ciarlet P. (Jr.), Labrunie S., “Theoretical tools to solve the axisymmetric Maxwell equations”, Math. Meth. Appl. Sci., 25 (2002), 49–78 | DOI | MR | Zbl

[3] Bernardi C., Dauge M., Maday Y., Spectral Methods for Axisymmetric Domains, Series in Appl. Math., 3, Gauthier-Villars, Paris – Amsterdam, 1999 | MR | Zbl

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

[5] Nikolskii S. M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1969 | MR

[6] Oganesyan L. A., Rukhovets L. A., Variatsionno-raznostnye metody resheniya ellipticheskikh uravnenii, Izd-vo AN ArmSSR, Erevan, 1979

[7] Babich V. M., “K voprosu o rasprostranenii funktsii”, Uspekhi matem. nauk, 8:2 (1953), 111–113 | MR | Zbl

[8] Kremer I. A., Urev M. V., “Raschet osesimmetrichnykh magnitnykh polei metodom konechnykh elementov”, Trudy Mezhdunarodnoi konferentsii po vychislitelnoi matematike MKVM-2004, Ch. II, Novosibirsk, 2004, 524–529