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:在这项工作中,我们为布林克曼问题制定了一种单独的方法,该方法在所有制度(由具有摩擦系数含义的本地层面无数字所确定)中都统一地以良好的方式处理,并且支持一般的网目和任意的近似命令。 该方法结合了高级奥氏和德赖姆混合法中的想法,其稳健性取决于潜在的重建和稳定条件,这些条件根据当地摩擦系数的价值而改变性质。 我们得出错误估计,由于存在截断因素,所有制度都有效,并提供了广泛的数字验证。</s>