Space-Time Residual-Based <italic>a posteriori</italic> Estimator for the <inline-formula> <tex-math notation="LaTeX">$A-\varphi$ </tex-math></inline-formula> Formulation in Eddy Current Problems

Abstract

In this paper, an a posteriori residual error estimator is presented for the 3-D eddy current problem modeled by the space-time A − ϕ potential formulation. It is solved by the finite element method in space and the backward Euler scheme in time. Once the reliability as well as the efficiency of the estimator is established, two numerical tests are proposed: 1) an analytical one to validate the theoretical results and 2) a physical one to illustrate the performance for a real eddy current problem.Index Terms-Eddy current, finite element (FE) analysis, potential formulation, space-time a posteriori estimators.