This work gives a general framework for the convergence analysis of low-order nonconforming elements for the 3D Brinkman model over cubical meshes, including the theory of uniform convergence with respect to the given parameters and the high accuracy analysis in the Darcy region. We apply our theory to three elements known in other literature and a newly constructed edge-face-based element to show their optimal approximation ability. Numerical examples are also provided to confirm our theory.

中文翻译：

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3D Brinkman 模型的低阶不合格砖单元

这项工作为立方网格上的 3D Brinkman 模型的低阶不符合元素的收敛分析提供了一个通用框架，包括关于给定参数的均匀收敛理论和达西区域的高精度分析。我们将我们的理论应用于其他文献中已知的三个元素和一个新构建的基于边缘面的元素，以显示它们的最佳逼近能力。还提供了数值例子来证实我们的理论。