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Variational subgrid scale formulations for the advection-diffusion-reaction equation. (English) Zbl 0996.76074

Summary: The exact variational multiscale (VMS) and the subgrid scale methods have been developed for advection-reaction and advection-diffusion-reaction equations. From the element Green’s 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 in the one-dimensional case.

MSC:

76M30 Variational methods applied to problems in fluid mechanics
76M10 Finite element methods applied to problems in fluid mechanics
76R99 Diffusion and convection
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