Geodesic
The convergence of finite element method for axially symmetric magnetostatic problem
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 9 (2006) no. 1, pp. 63-79

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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. 
@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},
     publisher = {mathdoc},
     volume = {9},
     number = {1},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2006_9_1_a6/}
}
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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/