Staggered finite element methods on polytopal meshes

We present a novel staggered discontinuous Galerkin method on general polytopal meshes for solving the shallow water equation on the sphere. Every polygon is decomposed into so called kite quads by joining the vertices with the midpoints of the adjacent edges and the midpoint of the polygon. The shallow water equation is solved in vector-invariant form whereby vorticity is determined diagnostically. Height and momentum are discretized on the primal respectively dual cells whereby the composed finite elements are continuous over internal edges and discontinuous over boundary edges. This results in block-diagonal mass matrices. Mass lumping can reduce the fill in of these matrices further. 
The method is implemented in Julia in the package CGDycore.jl which unifies different numerical dycores under one umbrella. Numerical results are presented for standard test cases on different spherical grids.