Convergence analysis of an adaptive edge element method for Maxwell's equations (Q731961)

The authors derive a posteriori estimates for solving the 3D static Maxwell equations using edge elements of Nedelec's first family. Based on these estimates, an adaptive edge element algorithm is proposed and its convergence is proved. The algorithm has the advantage that the usual marking of elements based on the oscillation is not needed, while linear convergence can be still proved in terms of the reduction of the energy norm error and the oscillation. Numerical examples demonstrate the efficiency and robustness of the method.