An Equilibrated Error Estimator for the 2-D/1-D MSFEM T-Formulation of the Eddy Current Problem

The 2-D/1-D multiscale finite element method (MSFEM) is an efficient way to simulate rotating machines in which each iron sheet is exposed to the same field. It allows the reduction of the 3-D sheet to a 2-D cross section by resolving the dependence along the thickness of the sheet with a polynomial expansion. This work presents an equilibrated error estimator based on flux equilibration and the theorem of Prager and Synge for the T-formulation of the eddy current problem in a 2-D/1-D MSFEM setting. The estimator is shown to give both a good approximation of the total error and to allow for adaptive mesh refinement by correctly estimating the local error distribution.