The discontinuous control-volume/finite-element method is applied to the
one-dimensional advection-diffusion equation. The aforementioned methodology
is relatively novel and has been mainly applied for the solution of
pure-advection problems. This work focuses on the main features of an accurate
representation of the diffusion operator, which are investigated both by
Fourier analysis and numerical experiments. A mixed formulation is followed,
where the constitutive equation for the diffusive flux is not substituted into
the conservation equation for the transported scalar. The Fourier analysis of
a linear, diffusion problem shows that the resolution error is both dispersive
and dissipative, in contrast with the purely dissipative error of the traditional
continuous Galerkin approximation.
