A multi-level discontinuous Galerkin method for solving the stationary Navier–Stokes equations

✍ Scribed by Yinnian He; Jian Li

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 249 KB
• Volume: 67
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2006.07.025

✦ Synopsis

In this paper, we consider the multi-level discontinuous finite element method for solving the stationary incompressible Navier-Stokes equations. On the coarsest mesh the discrete nonlinear Navier-Stokes equations are solved by using piecewise polynomial functions, which are totally discontinuous across inter-element boundaries and are pointwise divergence free on each element for the velocity and are continuous functions for the pressure. Subsequent approximations are generated on a succession of refined grids by solving the Newton linearized Navier-Stokes equations using piecewise polynomial functions which are similar to that on the coarsest mesh. Finally, the well-posedness and the optimal error estimate for the multi-level discontinuous Galerkin method are provided. The error analysis shows that when the mesh scales k j+1 = O(k 2 j ), h j+1 = O(h 2 j ) with j = 0, 1, . . . , J -1 are chosen, the multi-level finite element method can save a large amount of computational time compared with the one-level finite element method.