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

@article{Anaya2016APA,
  title={A priori and a posteriori error analysis of a mixed scheme for the Brinkman problem},
  author={Ver{\'o}nica Anaya and David Mora and Ricardo Oyarz{\'u}a and Ricardo Ruiz-Baier},
  journal={Numerische Mathematik},
  year={2016},
  volume={133},
  pages={781-817}
}
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 $$k \ge 0$$k≥0 for the approximation of the velocity field, piecewise continuous polynomials of degree $$k+1$$k+1 for the vorticity, and piecewise… 
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