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Numerical solution of transient eddy current problems with input current intensities as boundary data. (English) Zbl 1247.78035

Summary: The aim of this paper is to analyse a numerical method for the solution of transient eddy current problems with input current intensities as data, formulated in terms of the magnetic field in a bounded domain including conductors and dielectrics. To this end, we introduce a time-dependent weak formulation and prove its well-posedness. We propose a finite element method for space discretization based on the Nédélec edge elements on tetrahedral meshes, for which we obtain error estimates. Then, we introduce a backward Euler scheme for time discretization and prove error estimates for the fully discrete problem, too. Furthermore, a magnetic scalar potential is introduced to deal with the curl-free condition in the dielectric domain, which leads to an important saving in computational effort. Finally, the method is applied to solve two problems: a test with a known analytical solution and an application to electromagnetic forming.

MSC:

78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
78M30 Variational methods applied to problems in optics and electromagnetic theory
78M20 Finite difference methods applied to problems in optics and electromagnetic theory
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