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.

翻译：本文针对Brinkman问题发展了一种离散化方法，该方法在所有工况下（由具有摩擦系数含义的局部无量纲数定义）均具有均匀良好的表现，同时支持一般网格和任意逼近阶数。该方法结合了混合高阶方法和离散de Rham方法的思想，其鲁棒性依赖于势函数重构与稳定化项——这些项根据局部摩擦系数的值改变性质。我们推导了误差估计，由于截止因子的存在，该估计在所有工况下均成立，并提供了广泛的数值验证。