| Sumario: |
In this paper we present an a posteriori error analysis of a mixed-VEM discretization
for a nonlinear Brinkman model of porous media flow, which has been proposed
by the authors in a previous work. Therein, the system is formulated in terms of a
pseudostress tensor and the velocity gradient, whereas the velocity and the pressure of
the fluid are computed via postprocessing formulas. Furthermore, the well-posedness
of the associated augmented formulation along with a priori error bounds for the
discrete scheme also were established. We now propose reliable and efficient residualbased a posteriori error estimates for a computable approximation of the virtual
solution associated to the aforementioned problem. The resulting error estimator is
fully computable from the degrees of freedom of the solutions and applies on very
general polygonal meshes. For the analysis we make use of a global inf–sup condition,
Helmholtz decomposition, local approximation properties of interpolation operators and
inverse inequalities together with localization arguments based on bubble functions.
Finally, we provide some numerical results confirming the properties of our estimator
and illustrating the good performance of the associated adaptive algorithm
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