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A polytopal method for the Brinkman problem robust in all regimes

Jérôme Droniou
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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 cutoff factors, are valid across the all regimes and provide extensive numerical validation.
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Dates and versions

hal-03930849 , version 1 (09-01-2023)

Identifiers

  • HAL Id : hal-03930849 , version 1

Cite

Daniele Antonio Di Pietro, Jérôme Droniou. A polytopal method for the Brinkman problem robust in all regimes. 2023. ⟨hal-03930849⟩
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