H2-STABILITY OF SOME SECOND ORDER FULLY DISCRETE SCHEMES FOR THE NAVIER-STOKES EQUATIONS

This paper considers the H-2-stability results for the second order fully discrete schemes based on the mixed finite element method for the 2D time-dependent Navier-Stokes equations with the initial data u(0) is an element of H-alpha, where alpha = 0, 1 and 2. A mixed finite element method is used to the spatial discretization of the Navier-Stokes equations, and the temporal treatments of the spatial discrete Navier-Stokes equations are the second order semi-implicit, implicit/explict and explicit schemes. The H-2-stability results of the schemes are provided, where the second order semi-implicit and implicit/explicit schemes are almost unconditionally H-2-stable, the second order explicit scheme is conditionally H-2-stable in the case of alpha = 2, and the semi-implicit, implicit/explicit and explicit schemes are conditionally H-2-stable in the case of alpha = 1, 0. Finally, some numerical tests are made to verify the above theoretical results.