Error estimates of two-level finite element method for Smagorinsky model

Two-level finite element method for simulating Smagorinsky model in large eddy simulation is investigated. In this two-level algorithm, a linearized discrete problem is solved by using the variational multiscale method on the coarse mesh. Corresponding to Newton linearization method, the linearized Smagorinsky model is solved on the fine mesh. The error estimates derived in this paper implies that by choosing appropriate mesh sizes and the radius of the spatial filter used in Smagorinsky model, the two-level method provides the optimal convergence rates for the velocity in H1 norm and the pressure in L2 norm. Meanwhile, the two different numerical experiments are given to support the optimal convergence rates and the high efficiency of two-level algorithm.