  The aim of this paper is twofold. On the one hand, we test numerically the
performance of mixed virtual elements in three dimensions for the first time in
the literature to solve the mixed formulation of three-dimensional elliptic
equations on polyhedral meshes. On the other hand, we focus on the parallel
solution of the linear system arising from such discretization, considering
both direct and iterative parallel solvers. In the latter case, we develop two
block preconditioners, one based on the approximate Schur complement and one on
a regularization technique. Both these topics are numerically validated by
several parallel tests performed on a Linux cluster. More specifically, we show
that the proposed VEM discretization recovers the expected theoretical
convergence properties and we analize the performance of the direct and
iterative parallel solvers taken into account.
