Low-Order Nonconforming Brick Elements For The 3d Brinkman Model

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.