An interior penalty method for a two dimensional curl-curl and grad-div problem

We study an interior penalty method for a two dimensional curl-curl and grad-div problem that appears in electromagnetics and in fluid-structure interactions. The method uses discontinuous $P_1$~vector fields on graded meshes and satisfies optimal convergence rates (up to an arbitrarily small parameter) in both the energy norm and the $L_2$~norm. These theoretical results are corroborated by results of numerical experiments. References Th. Apel. Anisotropic Finite Elements . Teubner, Stuttgart, 1999. Th. Apel, A.-M. Saendig, and J.R. Whiteman. Graded mesh refinement and error estimates for finite element solutions of elliptic boundary value problems in non-smooth domains. Math. Methods Appl. Sci. , 19:63--85, 1996. F. Assous, P. Ciarlet, Jr., S. Labrunie, and J. Segre. Numerical solution to the time-dependent Maxwell equations in axisymmetric singular domains: the singular complement method. J. Comput. Phys. , 191:147--176, 2003. F. Assous, P. Ciarlet, Jr., E. Garcia, and J. 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