A polytopal method for the Brinkman problem robust in all regimes

Daniele Antonio Di Pietro (1) , Jérôme Droniou (2)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 Monash University [Clayton]

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 cutoff factors, are valid across the all regimes and provide extensive numerical validation.

Mots clés: Brinkman; Darcy; Stokes; Hybrid High-Order methods; Discrete de Rham methods

Domaines: Analyse numérique [math.NA]

Daniele Antonio Di Pietro, Jérôme Droniou. A polytopal method for the Brinkman problem robust in all regimes. Computer Methods in Applied Mechanics and Engineering, 2023, 409, pp.115981. ⟨10.1016/j.cma.2023.115981⟩. ⟨hal-03930849⟩