Stability of the residual free bubble method for bilinear finite elements on rectangular grids
Preprint series: 00-28, Preprints
- 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
- 65N12 Stability and convergence of numerical methods
Abstract: We consider the nature of the stabilizing term arising in the residual free bubble approach for piecewise bilinear functions on rectangular grids. We show, that on the subspace of piecewise linear functions the stabilizing term is identical to that in the streamline diffusion approach. However, on the space of piecewise bilinear functions there is a case in which the stabilizing term is weaker compared to the term used in the streamline diffusion method. In the particular case when the direction of the convection is directed parallel to a diagonal of the quadrilateral, control is lost over the mixed derivatives in the convection-dominated limit.
Keywords: finite element method, convection diffusion problem, residual free bubble approach
The author(s) agree, that this abstract may be stored asfull text and distributed as such by abstracting services.