  We consider the numerical approximation of single phase flow in porous media
by a mixed finite element method with mass lumping. Our work extends previous
results of Wheeler and Yotov, who showed that mass lumping together with an
appropriate choice of basis allows to eliminate the flux variables locally and
to reduced the mixed problem in this way to a finite volume discretization for
the pressure only. Here we construct second order approximations for hybrid
meshes in two and three space dimensions which, similar to the method of
Wheeler and Yotov, allows the local elimination of the flux variables. A full
convergence analysis of the method is given for which new arguments and, in
part, also new quadrature rules and finite elements are required. Computational
tests are presented for illustration of the theoretical results.
