In this paper, a new type of staggered discontinuous Galerkin methods for the three dimensional Maxwells equations is developed and analyzed. The spatial discretization is based on staggered Cartesian grids so that many good properties are obtained. First of all, our method has the advantages that the numerical solution preserves the electromagnetic energy and automatically fulfills a discrete version of the Gauss law. Moreover, the mass matrices are diagonal, thus time marching is explicit and is very efficient. Our method is high order accurate and the optimal order of convergence is rigorously proved. It is also very easy to implement due to its Cartesian structure and can be regarded as a generalization of the classical Yees scheme as well as the quadrilateral edge finite elements. Furthermore, a superconvergence result, that is the convergence rate is one order higher at interpolation nodes, is proved

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We introduce and study the Jarník limit set ℐ_{σ}of a geometrically finite Kleinian group with parabolic elements. The set ℐ_{σ}is the dynamical equivalent of the classical set of well approximable limit points. By generalizing the method of Jarník in the theory of Diophantine approximations, we estimate the dimension of ℐ_{σ}with respect to the Patterson measure. In the case in which the exponent of convergence of the group does not exceed the maximal rank of the parabolic fixed points, and hence in particular for all finitely generated Fuchsian groups, it is shown that this leads to a complete description of ℐ_{σ}in terms of Hausdorff dimension. For the remaining case, we derive some estimates for the Hausdorff dimension and the packing dimension of ℐ_{σ}.