An Equilibrated Error Estimator for the Multiscale Finite Element Method of a Linear Eddy Current Problem

Abstract

Abstract-The multiscale finite element method (MSFEM) is an efficient way to solve the eddy current problem on laminated iron cores without the necessity to resolve each laminate by the mesh. This paper presents an a posteriori error estimator for a MSFEM using the T-formulation of the eddy current problem. The estimator is based on flux equilibration and gives an upper bound for the error without generic constants. It requires the solution of small local problems on the fine scale.