Convergence analysis of a new multiscale finite element method for the stationary NavierStokes problem ?
In this paper, we propose a new multiscale finite element method for the stationary NavierStokes problem. This new method for the lowest equal order finite element pairs P1/P1 P 1 / P 1 is based on the multiscale enrichment and derived from the NavierStokes problem itself. Therefore, the new multiscale finite element method better reflects the nature of the nonlinear problem. The well-posedness of this new discrete problem is proved under the standard assumption. Meanwhile, convergence of the optimal order in the H1 H 1 -norm for the velocity and the L2 L 2 -norm for the pressure is obtained. Especially, via applying a new dual problem and some techniques in the process for proof, we establish the convergence of the optimal order in the L2 L 2 -norm for the velocity. Finally, numerical examples confirm our theory analysis and validate the effectiveness of this new method.
multiscale finite element method the navierstokes problem p1/p1 p 1 / p 1 elements p1/p1 p 1 / p 1 p1/p1 p 1 / p 1 p 1 / p 1 error analysis