Partial differential equations on hypergraphs and networks of surfaces: derivation and hybrid discretizations
Numerical Analysis
2022-07-04 v1 Numerical Analysis
Analysis of PDEs
Geometric Topology
Abstract
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).
Keywords
Cite
@article{arxiv.2108.06964,
title = {Partial differential equations on hypergraphs and networks of surfaces: derivation and hybrid discretizations},
author = {Andreas Rupp and Markus Gahn and Guido Kanschat},
journal= {arXiv preprint arXiv:2108.06964},
year = {2022}
}