Variational subgrid scale formulations for the advection–diffusion-reaction equation Original Research Article

The exact variational multiscale (VMS) and the subgrid scale (SGS) methods have been developed for the advection-reaction and the advection–diffusion-reaction equations. From the element Greenʹs function, approximate intrinsic time scale parameters have been derived for these cases and are shown to be similar to other expressions obtained in the literature out of the maximum principle and convergence/error analysis. The methods have been compared with typical stabilized finite element methods. As expected, the VMS is nodally exact for the one-dimensional case.