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Zbl 0902.65078
Melkes, F.; Ženíšek, A.
On a certain two-sided symmetric condition in magnetic field analysis and computations. (English)
[J] Appl. Math., Praha 42, No.2, 147-159 (1997). ISSN 0862-7940; ISSN 1572-9109/e

A finite element method for solving a nonlinear boundary value problem of elliptic type with mixed boundary conditions is investigated. The problem describes the nonlinear stationary magnetic field distributed in a planar domain composed of different isotropic media. The authors introduce a special two-sided condition for the incremental magnetic reductivity which guarantees the existence and uniqueness of the weak and approximate solutions. The main theorem establishes the convergence of the finite element method in the Sobolev $H^1(\Omega)$-norm. A numerical example for the calculation of a magnetic potential in a synchronous rotary machine is given.
[M.Křížek (Praha)]

MSC 2000:: *65Z05 Applications to physics
65N30 Finite numerical methods (BVP of PDE)
65N12 Stability and convergence of numerical methods (BVP of PDE)
35Q60 PDE of electromagnetic theory and optics
78A30 Electro- and magnetostatics

Keywords: magnetic field; variational formulation; convergence; finite element method; numerical example; magnetic potential

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