Abstract
In this paper we discuss the design and analysis of a class of stabilization operators for space-time Galerkin least-squares finite element discretizations suitable for the incompressible limit of the symmetrized Navier-Stokes equations given in [G. Hauke, T.J.R. Hughes, A comparative study of different sets of variables for solving compressible and incompressible flows, Comput. Methods Appl. Mech. Engrg. 153 (1998) 1-44]. This set of equations consists of the incompressible Navier-Stokes equations in combination with the heat equation. The analysis results in stabilization operators which are positive definite and dimensionally consistent. In addition, a detailed proof is given that the space-time Galerkin least squares discretization together with the proposed stabilization operators satisfies a coercivity condition for the linearized form of the equations. This ensures that necessary conditions for uniqueness and stability of the numerical solution are satisfied by the finite element discretization.
| Original language | English |
|---|---|
| Pages (from-to) | 982-1006 |
| Number of pages | 25 |
| Journal | Computer methods in applied mechanics and engineering |
| Volume | 195 |
| Issue number | 9-12 |
| DOIs | |
| Publication status | Published - 2006 |
Keywords
- Galerkin methods
- Stabilization
- vortex induced vibrations
- MSC-65M60
- MSC-76M10