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The convergence of finite element method for axially symmetric magnetostatic problem. (Russian. English summary) Zbl 1115.78011
Summary: We consider a problem of calculation of stationary magnetic linear axially symmetric fields in nonhomogeneous media. As distinct from conventional formulations of this problem in terms of the azimuthal vector potential component or a function of magnetic field flow, we offer the reduction to another sought for function satisfying the equation to be most convenient for investigation. The principal feature of the problem 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.

78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
78A30 Electro- and magnetostatics
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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