The paper deals with some mixed finite element methods on a class
of anisotropic meshes based on tetrahedra and prismatic (pentahedral)
elements. Anisotropic local
interpolation error estimates are derived in some anisotropic weighted Sobolev
spaces. As particular
applications, the numerical approximation by mixed methods of the Laplace equation
in domains
with edges is investigated where anisotropic finite
element meshes are appropriate. Optimal error estimates are obtained using
some anisotropic regularity results of the
solutions.