  We investigate the piecewise linear nonconforming Crouzeix-Raviar and the
lowest order Raviart-Thomas finite-element methods for the Poisson problem on
three-dimensional anisotropic meshes. We first give error estimates of the
Crouzeix-Raviart and the Raviart-Thomas finite-element approximate problems. We
next present the equivalence between the Raviart-Thomas finite-element method
and the enriched Crouzeix-Raviart finite-element method. We emphasise that we
do not impose either shape-regular or maximum-angle condition during mesh
partitioning. Numerical results confirm the results that we obtained.
