Adaptive Edge Element Methods in 3D Electromagnetic Field Computation

Ronald H.W. Hoppe

Dept. of Math., Univ. of Houston, Houston, TX 77204-3008, U.S.A. and Inst. of Math., Univ. of Augsburg, D-86159 Augsburg, Germany

We consider Adaptive Edge Finite Element Methods (AEFEM) for the 3D eddy currents equations with variable coefficients based on the lowest order edge elements of Nedelec's first family with respect to an adaptively generated hierarchy of simplicial triangulations. The mesh adaptivity relies on a residual-type a posteriori error estimator featuring face and element residuals. Both the components of the estimator and certain oscillation terms, due to the occurrence of the variable coefficients, have to be controlled properly within the adaptive loop which is taken care of by appropriate bulk criteria. Convergence of the AEFEM in terms of reductions of the energy norm of the discretization error and of the oscillations is shown. Numerical results are given to illustrate the performance of the AEFEM.