A priori and a posteriori error analysis of a mixed scheme for the Brinkman problem

Verónica Anaya, David Mora, Ricardo Oyarzúa, Ricardo Ruiz-Baier
2015 Numerische Mathematik  
This paper deals with the analysis of new mixed finite element methods for the Brinkman equations formulated in terms of velocity, vorticity and pressure. Employing the Babuška-Brezzi theory, it is proved that the resulting continuous and discrete variational formulations are well-posed. In particular, we show that Raviart-Thomas elements of order k ≥ 0 for the approximation of the velocity field, piecewise continuous polynomials of degree k + 1 for the vorticity, and piecewise polynomials of
more » ... gree k for the pressure, yield unique solvability of the discrete problem. On the other hand, we also show that families of finite elements based on Brezzi-Douglas-Marini elements of order k +1 for the approximation of velocity, piecewise continuous polynomials of degree k +2 for the vorticity, and piecewise polynomials of degree k for the pressure ensure the well-posedness of the associated Galerkin scheme. We note that these families provide exactly divergence-free approximations of the velocity field. We establish a priori error estimates in the natural norms with constants independent B Ricardo Ruiz-Baier
doi:10.1007/s00211-015-0758-x fatcat:q4cxwhjbtrf2lho5pn4moy46qi