The 2D/1D 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 three dimensional sheet to a two dimensional 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 2D/1D 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.

翻译：二维/一维多尺度有限元法(MSFEM)是模拟每层硅钢片暴露于相同磁场中旋转电机的一种高效方法。该方法通过多项式展开解析沿厚度方向的依赖关系,将三维硅钢片降维为二维横截面。本文针对二维/一维MSFEM框架下涡流问题的T公式,提出了一种基于通量平衡及Prager-Synge定理的平衡误差估计量。研究表明,该估计量既能精确逼近总误差,又可通过准确估计局部误差分布实现自适应网格细化。