In this paper, we propose, analyze and validate a new skew-symmetric Nitsche's scheme for the Brinkman problem with mixed Dirichlet-Neumann boundary conditions and non-null sources terms. Based on an augmented formulation where pseudostress and velocity are treated as unknowns, we impose the Neumann boundary conditions using Nitsche terms. The proposed scheme does not require the introduction of additional unknowns and the stability analysis is established using an energy norm. This new augmented scheme employs Raviart-Thomas elements for the approximation of the pseudostress and Lagrange finite elements for the approximation of the fluid velocity. Assuming classical regularity assumptions, well-posedness, and optimal convergence of the scheme are proved. Several computational experiments in two and three dimensions illustrate the effectiveness of the proposed scheme.
Cárcamo et al. (Fri,) studied this question.