A Posteriori Error Estimator for Finite Element Simulation of Electromagnetic Material Processing

This article focuses on the development of error estimators for evaluating the accuracy of finite-element computations of the electromagnetic phenomena for electromagnetic material processing modeling. The ultimate goal of this work is to enable adaptive anisotropic remeshing in order to reach a prescribed accuracy. We first introduce a numerical model based on the quasi-steady-state approximation of the Maxwell's equations in a time-domain formalism. We then introduce an estimator based on a recovery method; its results will be compared with other estimators based on investigating how accurately some of the electromagnetic equations are checked. The estimators are then validated on analytical cases; an additional application to a complex case shows the robustness of our approach. Scientific advances of this work include the development of a robust field recovery strategy for error computation, as well as the introduction of a general purpose error normalization scheme which overcomes field scale bias enabling seamless comparison of errors from different physical fields.