In this paper we systematically review
the control volume finite element (CVFE) methods for numerical
solutions of second-order partial differential equations.
Their relationships to the finite difference
and standard (Galerkin) finite element methods are considered.
Through their relationship
to the finite differences, upstream weighted
CVFE methods and the conditions on positive
transmissibilities (positive flux linkages)
are studied. Through their relationship
to the standard finite elements,
error estimates for
the CVFE are obtained. These estimates are
comparable to those for the standard finite element methods
using piecewise linear elements. Finally, an
application to multiphase flows in porous
media is presented.