A NONCONFORMING PENALTY METHOD FOR A TWO-DIMENSIONAL CURL-CURL PROBLEM

A nonconforming finite element method for a two-dimensional curl-curl problem is studied in this paper. It uses weakly continuous P(1) vector fields and penalizes the local divergence. Two consistency terms involving the jumps of the vector fields across element boundaries are also included to ensure the convergence of the scheme. Optimal convergence rates ( up to an arbitrary positive epsilon) in both the energy norm and the L(2) norm are established on graded meshes. This scheme can also be used in the computation of Maxwell eigenvalues without generating spurious eigenmodes. The theoretical results are confirmed by numerical experiments.