A Convergence Study of the 3D Dynamic Diffusion Method

In this work we present a convergence study of the multiscale Dynamic Diffusion (DD) method applied to the three-dimensional steady-state transport equation. We consider diffusion-convection and diffusion-convection-reaction problems, varying the diffusion coefficient in order to obtain an increasingly less diffusive problem. For both cases, the convergence order estimates are evaluated in the energy norm and the \(L^2(\varOmega )\) and \(H^1(\varOmega )\) Sobolev spaces norms. In order to investigate the meshes effects on the convergence, the numerical experiments were carried out on two different sets of meshes: one with structured meshes and the other with unstructured ones. The numerical results show optimal convergence rates in all norms for the dominant convection case.