On a certain two-sided symmetric condition in magnetic field analysis and computations. (English) Zbl 0902.65078

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.


65Z05 Applications to the sciences
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
78A30 Electro- and magnetostatics
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