NUMERICAL ANALYSIS OF A BDF2 FINITE ELEMENT SCHEME FOR NAVIER-STOKES-ALPHA MODEL

In this paper, we study a second-order backward difference formula (BDF2) scheme for the Navier-Stokes-alpha model. We combine a stabilized finite element discretization in space with the BDF2 method in time to obtain a fully discrete approximation. A complete numerical analysis is presented, establishing unconditional stability and deriving optimal-order error estimates for the scheme. Numerical experiments are provided to verify the theoretical results and to illustrate the effectiveness of the proposed approach.