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

TL;DR

This paper introduces an equilibrated error estimator for the 2D/1D MSFEM T-formulation of the eddy current problem, enabling accurate error assessment and adaptive mesh refinement in simulations of rotating machines.

Contribution

It presents a novel equilibrated error estimator based on flux equilibration for the 2D/1D MSFEM T-formulation, improving error estimation and adaptivity.

Findings

Estimator accurately approximates total error

Supports effective adaptive mesh refinement

Demonstrates reliability in 2D/1D MSFEM simulations

Abstract

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.