  We introduce a general, analytical framework to express and to approximate
partial differential equations (PDEs) numerically on graphs and networks of
surfaces---generalized by the term hypergraphs. To this end, we consider PDEs
on hypergraphs as singular limits of PDEs in networks of thin domains (such as
fault planes, pipes, etc.), and we observe that (mixed) hybrid formulations
offer useful tools to formulate such PDEs. Thus, our numerical framework is
based on hybrid finite element methods (in particular, the class of hybrid
discontinuous Galerkin methods).
