3. 1. 4 Conclusion

One major advantage of the formalism according to Chapter 2 is that the requirements on the underlying structures as well as the complexity can be seen easily. While the initial formulation using the indices $i$ and $j$ does not necessarily reveal the actual nature of the traversal of the underlying topological complex, the final formulation gives a precise definition of the topological traversal functions required for the implementation of the traversal.

In order to deal with higher-order schemes, it is necessary to use functions which traverse all cells which are incident to an element and traversal schemes which traverse all elements which are incident to one cell. Furthermore, it has to be considered that on one element two values of one quantity can be located, if more collocation points are in the interior of this element.