Partial differential equations on hypergraphs and networks of surfaces: derivation and hybrid discretizations

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