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：本文针对布林克曼问题提出了一种离散化方法，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表征）均能保持一致性良好行为，支持通用网格划分及任意逼近阶数。该方法融合了混合高阶方法与离散德拉姆方法的思想，其鲁棒性建立在势重构与稳定化项的基础上——这些项会随局部摩擦系数的取值变化而发生本质改变。我们推导了误差估计，这些估计借助截断因子在所有工况下均有效，并通过大量数值实验进行了验证。