Based on two-grid discretizations, in this paper, some new local and parallel finite element algorithms are proposed and analyzed for the stationary incompressible Navier-Stokes problem. These algorithms are motivated by the observation that for a solution to the Navier-Stokes problem, low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on a fine grid by some local and parallel procedure. One major technical tool for the analysis is some local a priori error estimates that are also obtained in this paper for the finite element solutions on general shape-regular grids.
|Original language||English (US)|
|Number of pages||12|
|Journal||Journal of Computational Mathematics|
|State||Published - May 2006|
All Science Journal Classification (ASJC) codes
- Applied Mathematics
- Computational Mathematics