A nonconforming rectangular finite element pair for the Darcy-Stokes-Brinkman model

In this article, we consider the Darcy-Stokes-Brinkman model that can be sorted into three problems: the Darcy problems, the Stokes-Brinkman interface problems and the coupled Darcy-Stokes problems. We study finite element approximation of the model with Dirichlet boundary conditions and make a unified analysis of the three problems based on nonconforming element. Optimal error estimates for the fluid velocity and pressure are derived. Finally, we present some numerical examples verifying the theoretical predictions.