Stability of the residual free bubble method for bilinear finite elements on rectangular grids

IMA Journal of Numerical Analysis

Volumn 22, Issue 1, 2002, Pages 73-87

  Franca, Leopoldo P ^a   Tobiska, Lutz ^b  

^a UNIVERSITY OF COLORADO   (United States)

^b OTTO VON GUERICKE UNIVERSITY   (Germany)

Author keywords

Residual free bubble; Stability; Streamline diffusion

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; PIECEWISE LINEAR TECHNIQUES;

BILINEAR FUNCTIONS; CONVECTION-DOMINATED; MIXED DERIVATIVES; PIECE-WISE LINEAR FUNCTIONS; RECTANGULAR GRIDS; RESIDUAL FREE BUBBLES; STREAMLINE DIFFUSION; STREAMLINE DIFFUSION METHODS;

DIFFUSION;

EID: 0036100663     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/22.1.73     Document Type: Article

References (13)

1. BAIOCCHI, C., BREZZI, F. & FRANCA, L. P. 1993 Virtual bubbles and Galerkin-least-squares type methods (Ga.L.S.). Comput. Meth. Appl. Mech. Eng., 105, 125-141.
2. BREZZI, F., BRISTEAU, M.-O., FRANCA, L. P., MALLET, M. & ROGÉ, G. 1992 A relationship between stabilized finite element methods and the Galerkin method with bubble functions. Comput. Meth. Appl. Mech. Eng., 96, 117-129.
3. BREZZI, F., FRANCA, L. P. & Russo, A. 1998 Further considerations on residual-free bubbles for advective-diffusive equations. Comput. Meth. Appl. Mech. Eng., 166, 25-33.
4. BREZZI, F., HUGHES, T. J. R., MARINI, L. D., Russo, A. & SÜLI, E. 1999 A priori error analysis of residual-free bubbles for the advection-diffusion problems. SIAM J. Numer. Anal., 36, 1933-1948.
5. BREZZI, F., MARINI, L. D. & SÜLI, E. 2000 Residual-free bubbles for advection-diffusion problems: the general error analysis. Numer. Math., 85, 31-47.
6. DE JAGER, E. M. & FURU, J. 1996 The Theory of Singular Perturbations, Applied Mathematics and Mechanics, vol. 42. Amsterdam: Elsevier.
7. FRANCA, L. P. & FREY, S. L. 1992 Stabilized finite element methods: II. The incompressible Navier-Stokes equations. Comput. Meth. Appl. Mech. Eng., 99, 209-233.
8. FRANCA, L. P., NESLITURK, A. & STYNES, M. 1998 On the stability of residual-free bubbles for convection-diffusion problems and their approximation by a two-level finite element method. Comput. Meth. Appl Mech. Eng., 166, 35-49.
9. GILBARG, D. & TRUDINGER, N. S. 1998 Elliptic Partial Differential Equations of Second Order, Number 224 in Grundlehren der mathematischen Wissenschaften. Berlin: Springer.
10. GOERING, H., FELGENHAUER, A., LUBE, G., ROOS, H.-G. & TOBISKA, L. 1983 Singularly Perturbed Differential Equations, Mathematical Research, vol. 13. Berlin: Akademie.
11. KNOBLOCH, P. Reduced finite element discretizations of the Stokes and Navier-Stokes equations. J. Math. Fluid Mech. To appear.
12. 1-element applied to the incompressible Navier-Stokes equations. Math. Modelling Numer. Anal., 34, 85-107.
13. RUSSO, A. 1996 Bubble stabilization of finite element methods for the linearized incompressible Navier-Stokes equations. Comput. Meth. Appl. Mech. Eng., 132, 335-343.