High accuracy analysis of the reduced Adini–Stokes element for the Brinkman model

This work provides a high accuracy analysis of the reduced Adini–Stokes element method developed in [7] for the Brinkman model. We show that this method is uniformly convergent for the velocity with convergence order $O(h^2)$ in a mesh- and parameter-dependent norm over general quasi-uniform rectangular meshes. A proper postprocessing technique is also proposed to improve the precision of the pressure. Numerical examples confirm our theory.