Superclose and superconvergence of finite element discretizations for the Stokes equations with damping

A class of conforming mixed finite element methods (FEMs) are applied to the Stokes equations with damping. With the help of the prior estimates for the exact and approximated solutions and the appropriate choice of the parameters α,ν and r appeared in the problem, the superclose and superconvergence results for the velocity in H1-norm and the pressure in L2-norm are derived. To our best knowledge, this is the first superconvergence analysis of conforming mixed FEMs for this kind nonlinear problem.