Subgridscale stabilization of time-dependent convection dominated diffusive transport

In [W.J. Layton, A connection between subgrid scale eddy viscosity and mixed methods, Appl. Math. Comput. 133 (2002) 147–157], a variationally consistent eddy viscosity discretization is given for the stationary convection diffusion equation. We further develop this discretization to include the time-dependent problem. We give comprehensive stability and error analysis of the semi-discrete case. We also state the stability and error results for the fully discrete algorithm with a Crank–Nicholson time discretization. The error bound is near optimal and independent of the diffusion coefficient, ϵ. Finally, we give guidance on optimal parameter selection for some common finite element spaces.