  This work combines the consistency in lower-order differential operators with
external approximations of functional spaces to obtain error estimates for
finite difference finite volume schemes on unstructured non-uniform meshes.
This combined approach is first applied to the one-dimensional elliptic
boundary value problem on non-uniform meshes, and a first-order convergence
rate is obtained, which agrees with the results previously reported. The
approach is also applied to the staggered MAC scheme for the two-dimensional
incompressible Stokes problem on unstructured meshes. A first-order convergence
rate is obtained, which improves over a previously reported result in that it
also holds on unstructured meshes. For both problems considered in this work,
the convergence rate is one order higher on meshes satisfying special
requirements.
