Abstract

In this work, we present the analysis of a Nitsche-based finite element method for the Brinkman equations written in terms of velocity and pressure. We provide a new discrete variational formulation that enables the weak imposition of mixed and non-standard boundary conditions, through a consistent and stable Nitsche method. The method is analyzed within the framework of Babu & scaron;ka-Brezzi theory, ensuring the well-posedness of the discrete problem. We derive a priori error estimates for the discrete scheme with constants independent of the viscosity. Finally, we present some numerical experiments to validate the theoretical results and assess the robustness of the proposed scheme.