Discontinuous control-volume/finite-element method for advection–diffusion problems

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.

► The discontinuous CVFEM method is applied to the advection–diffusion equation.
► A formal derivation of the method is provided.
► A detailed Fourier analysis is performed.
► Numerical simulations confirm the theoretical results.