Title:       A locally divergence-free nonvonforming finite element 
             method for the reduced time-harmonic Maxwell equation
 
Authors:     Susanne C. Brenner, Fengyan Li and Li-yeng Sung 

Status:      Submitted

Abstract:   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  Crouzeix-Raviart 
            nonconforming $P_1$ 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 $\epsilon$) in both the energy norm and the $L_2$ 
            norm are established on graded meshes.  The theoretical 
            results are confirmed by numerical experiments.