Geodesic
Solution of a~regularized problem for a~stationary magnetic field in a~non-homogeneous conducting medium by a~finite element method
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 13 (2010) no. 1, pp. 33-49

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In this paper, we substantiate the use of a vector finite element method for solving a regularized stationary magnetic problem, which is formulated in terms of a vector magnetic potential. To approximate the generalized solution, we make use of the Nedelec second kind vector elements of first order on tetrahedrons. Existence and uniqueness of the solution to a discrete regularized problem and its convergence to a generalized solution for the case of an inhomogeneous domain (according to electromagnetic properties) are justified. Some issues of the numerical solution to a discrete regularized problem are discussed. Approaches to optimize the algorithms are shown on a series of numerical experiments. 
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     title = {Solution of a~regularized problem for a~stationary magnetic field in a~non-homogeneous conducting medium by a~finite element method},
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I. A. Kremer; M. V. Urev. Solution of a~regularized problem for a~stationary magnetic field in a~non-homogeneous conducting medium by a~finite element method. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 13 (2010) no. 1, pp. 33-49. http://geodesic.mathdoc.fr/item/SJVM_2010_13_1_a3/