A nonconforming finite element method for the stationary Smagorinsky model

摘要

In this paper, we focus on a low order nonconforming finite element method (FEM) for the stationary Smagorinsky model. The velocity and pressure are approximated by the constrained nonconforming rotated Q1 element (CN Q1rot) and piecewise constant element, respectively. Optimal error estimates of the velocity in the broken H1-norm and L2-norm, and the pressure in the L2-norm are derived by some nonlinear analysis techniques and Aubin-Nitsche duality argument. The supercloseness and superconvergent results are also obtained under some reasonable regularity assumptions. Finally, a numerical example is implemented to confirm our theoretical analysis.