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A numerical method for a two-dimensional curl-curl and grad-div problem is studied in this paper. It is based on a discretization using weakly continuous P 1 vector fields and includes two consistency terms 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 L 2 norm are established on graded meshes. The theoretical results are confirmed by numerical experiments.

We study a class of symmetric discontinuous Galerkin methods on graded meshes. Optimal order error estimates are derived in both the energy norm and the L 2 norm, and we establish the uniform convergence of V -cycle, F-cycle and W -cycle multigrid algorithms for the resulting discrete problems. Numerical results that confirm the theoretical results are also presented.