We describe an abstract interface for the geometric coupling of finite element grids. The scope of the interface encompasses a wide range of domain decomposition techniques in use today, including nonconforming grids and grids of different dimensions. The couplings are described as sets of remote intersections, which encapsulate the relationships between pairs of elements on the coupling interface.

The abstract interface is realized in a module dune-grid-glue for the software framework dune. Several implementations of this interface exist, including one for general nonconforming couplings and a special efficient implementation for conforming interfaces. We present two numerical examples to show the flexibility of the approach.