Superconvergence Analysis of Low Order Nonconforming Mixed Finite Element Methods for Time-Dependent Navier-Stokes Equations

Abstract

In this paper, the superconvergence properties of the time-dependent Navier-Stokes equations are investigated by a low order nonconforming mixed finite element method (MFEM). In terms of the integral identity technique, the superclose error estimates for both the velocity in broken $H^1$-norm and the pressure in $L^2$-norm are first obtained, which play a key role to bound the numerical solution in $L^{\infty}$-norm. Then the corresponding global superconvergence results are derived through a suitable interpolation postprocessing approach. Finally, some numerical results are provided to demonstrate the theoretical analysis.