  The focus of the present paper is on developing a Virtual Element Method for
Darcy and Brinkman equations. In [15] we presented a family of Virtual Elements
for Stokes equations and we defined a new Virtual Element space of velocities
such that the associated discrete kernel is pointwise divergence-free. We use a
slightly different Virtual Element space having two fundamental properties: the
L^2-projection onto P_k is exactly computable on the basis of the degrees of
freedom, and the associated discrete kernel is still pointwise divergence-free.
The resulting numerical scheme for the Darcy equation has optimal order of
convergence and H^1 conforming velocity solution. We can apply the same
approach to develop a robust virtual element method for the Brinkman equation
that is stable for both the Stokes and Darcy limit case. We provide a rigorous
error analysis of the method and several numerical tests.
