A polytopal method for the Brinkman problem robust in all regimes
Numerical Analysis
2023-03-22 v3 Numerical Analysis
Abstract
In this work we develop a discretisation method for the Brinkman problem that is uniformly well-behaved in all regimes (as identified by a local dimensionless number with the meaning of a friction coefficient) and supports general meshes as well as arbitrary approximation orders. The method is obtained combining ideas from the Hybrid High-Order and Discrete de Rham methods, and its robustness rests on a potential reconstruction and stabilisation terms that change in nature according to the value of the local friction coefficient. We derive error estimates that, thanks to the presence of cut-off factors, are valid across the all regimes and provide extensive numerical validation.
Cite
@article{arxiv.2301.03272,
title = {A polytopal method for the Brinkman problem robust in all regimes},
author = {Daniele A. Di Pietro and Jérôme Droniou},
journal= {arXiv preprint arXiv:2301.03272},
year = {2023}
}