A locally divergence-free nonconforming finite element method for the time-harmonic Maxwell equations

A new numerical method for computing the divergence-free part of the solution of the time-harmonic Maxwell equations is studied in this paper. It is based on a discretization that uses the locally divergence-free CrouzeixRaviart nonconforming P1 vector fields and includes a consistency term involving the jumps of the vector fields across element boundaries. Optimal convergence rates (up to an arbitrary positive ) in both the energy norm and the L2 norm are established on graded meshes. The theoretical results are confirmed by numerical experiments.