An analysis of Nédélec's method for the spatial discretization of Maxwell's equations

AbstractIn 1980 Nédélec developed a family of curl- and divergence-conforming finite elements in R3. He proposed the use of these elements to discretize the time-dependent Maxwell equations, noting that the elements have the advantage that the discrete magnetic displacement can be made exactly divergence-free. In this paper, we shall analyze a slight generalization of Nédélec's scheme and prove essentially optimal-order convergence estimates in a variety of situations. We also demonstrate that the Nédélec method can be superconvergent at certain special points and we relate the method to Yee's finite-difference scheme. A by-product of our analysis will be a convergence proof for Yee's method