High Accuracy Analysis of the Reduced Adini Stokes Element for the Brinkman Model

This work provides the 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 the 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.