Computer Methods in Applied Mechanics and Engineering
Computer Methods in Applied Mechanics and Engineering
Error analysis of some Galerkin least squares methods for the elasticity equations
SIAM Journal on Numerical Analysis
Analysis of a streamline diffusion finite element method for the Stokes and Navier-Stokes equations
SIAM Journal on Numerical Analysis
Stabilized Finite Element Methods Based on Multiscale Enrichment for the Stokes Problem
SIAM Journal on Numerical Analysis
Consistent Local Projection Stabilized Finite Element Methods
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms
Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms
| Hi-index | 0.09 |
In this paper, we propose a new multiscale finite element method for the stationary Navier-Stokes problem. This new method for the lowest equal order finite element pairs P"1/P"1 is based on the multiscale enrichment and derived from the Navier-Stokes 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 H^1-norm for the velocity and the 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 L^2-norm for the velocity. Finally, numerical examples confirm our theory analysis and validate the effectiveness of this new method.