Second-Order Convergence Of The Linearly Extrapolated Crank-Nicolson Method For The Navier-Stokes Equations With H-1 Initial Data

This article concerns the numerical approximation of the two-dimensional nonstationary Navier-Stokes equations with H-1 initial data. By utilizing special locally refined temporal stepsizes, we prove that the linearly extrapolated Crank-Nicolson scheme, with the usual stabilized Taylor-Hood finite element method in space, can achieve second-order convergence in time and space. Numerical examples are provided to support the theoretical analysis.