Artículos de revistas
Analysis of an augmented pseudostress-based mixed formulation for a nonlinear Brinkman model of porous media flow
Registro en:
Computer Methods in Applied Mechanics and Engineering 289
0045-7825
Autor
Gatica, Gabriel N.
Gatica, Luis F.
Sequeira, Filander A.
Resumen
Artículo de publicación ISI In this paper we introduce and analyze an augmented mixed finite element method for the twodimensional
nonlinear Brinkman model of porous media flow with mixed boundary conditions.
More precisely, we extend a previous approach for the respective linear model to the present nonlinear
case, and employ a dual-mixed formulation in which the main unknowns are given by the
gradient of the velocity and the pseudostress. In this way, and similarly as before, the original
velocity and pressure unknowns are easily recovered through a simple postprocessing. In addition,
since the Neumann boundary condition becomes essential, we impose it in a weak sense, which
yields the introduction of the trace of the fluid velocity over the Neumann boundary as the associated
Lagrange multiplier. We apply known results from nonlinear functional analysis to prove that
the corresponding continuous and discrete schemes are well-posed. In particular, a feasible choice of
finite element subspaces is given by Raviart-Thomas elements of order k ≥ 0 for the pseudostress,
piecewise polynomials of degree ≤ k for the gradient, and continuous piecewise polynomials of
degree ≤ k + 1 for the Lagrange multiplier. We also derive a reliable and efficient residual-based a
posteriori error estimator for this problem. Finally, several numerical results illustrating the performance
and the robustness of the method, confirming the theoretical properties of the estimator,
and showing the behaviour of the associated adaptive algorithm, are provided.