| Issue |
ESAIM: M2AN
Volume 56, Number 2, March-April 2022
|
|
|---|---|---|
| Page(s) | 505 - 528 | |
| DOI | https://doi.org/10.1051/m2an/2022011 | |
| Published online | 24 February 2022 | |
Partial differential equations on hypergraphs and networks of surfaces: Derivation and hybrid discretizations
1
School of Engineering Science, Lappeenranta–Lahti University of Technology, P.O. Box 20, 53851 Lappeenranta, Finland
2
Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University, Mathematikon, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
* Corresponding author: kanschat@uni-heidelberg.de
Received:
6
September
2021
Accepted:
25
January
2022
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).
Mathematics Subject Classification: 65M60 / 65N30 / 68N30 / 53Z99 / 57N99
Key words: Conservation equations / hypergraphs / hybrid discontinuous Galerkin
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.