Solution of a regularized problem for a stationary magnetic field in a non-homogeneous conducting medium by a finite element method

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.