Bermúdez, Alfredo; López-Rodríguez, Bibiana; Rodríguez, Rodolfo; Salgado, Pilar Numerical solution of transient eddy current problems with input current intensities as boundary data. (English) Zbl 1247.78035 IMA J. Numer. Anal. 32, No. 3, 1001-1029 (2012). 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. Cited in 6 Documents 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 Keywords:eddy current problems; time-dependent electromagnetic problems; input current intensities; finite elements PDFBibTeX XMLCite \textit{A. Bermúdez} et al., IMA J. Numer. Anal. 32, No. 3, 1001--1029 (2012; Zbl 1247.78035) Full Text: DOI