Convergence analysis of an adaptive edge finite element method for the 2D eddy current equations

Abstract

For the 2D eddy currents equations, we design an adaptive edge finite element method (AEFEM) that guarantees an error reduction of the global discretization error in the H (curl)-norm and thus establishes convergence of the adaptive scheme. The error reduction property relies on a residual-type a posteriori error estimator and is proved for discretizations based on the lowest order edge elements of Nédélec's first family. The main ingredients of the proof are the reliability and the strict discrete local efficiency of the estimator as well as the Galerkin orthogonality of the edge element approximation.