Edge stabilization for the generalized Stokes problem: A continuous interior penalty method

Computer Methods in Applied Mechanics and Engineering

Volumn 195, Issue 19-22, 2006, Pages 2393-2410

  Burman, Erik ^a   Hansbo, Peter ^b  

^a EPFL   (Switzerland)

^b CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

Finite element; Generalized Stokes' equation; Gradient jumps; Inf sup condition; Interior penalty method; Stabilized methods

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; GALERKIN METHODS; GRADIENT METHODS; LEAST SQUARES APPROXIMATIONS; OPTIMIZATION;

GENERALIZED STOKES EQUATION; GRADIENT JUMPS; INTERIOR PENALTY METHOD; STABILIZED METHODS;

FINITE ELEMENT METHOD;

CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; GALERKIN METHODS; GRADIENT METHODS; LEAST SQUARES APPROXIMATIONS; OPTIMIZATION;

EID: 33644586167     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2005.05.009     Document Type: Article

References (23)

1. G.A. Baker Finite element methods for elliptic equations using nonconforming elements Math. Comp. 31 1977 45-59
2. R. Becker M. Braack A finite element pressure gradient stabilization for the Stokes equation based on local projection Calcolo 38 2001 173-199
3. H. Blank M. Rudgyard A. Wathen Stabilised finite element methods for steady incompressible flow Comput. Methods Appl. Mech. Engrg. 174 1999 91-105
4. F. Brezzi M. Fortin A minimal stabilisation procedure for mixed finite element methods Numer. Math. 89 2001 457-491
5. F. Brezzi M. Fortin Mixed and Hybrid Finite Element Methods 1991 Springer Berlin
6. F. Brezzi T.J.R. Hughes L.D. Marini A. Russo E.A. Süli A priori error analysis of residual-free bubbles for advection-diffusion problems SIAM J. Numer. Anal. 36 1999 1933-1948
7. E. Burman, P. Hansbo, Stabilized Crouzeix-Raviart element for the Darcy-Stokes Problem, PREPRINT Chalmers Finite Element Center, 2003-15.
8. F. Brezzi J. Pitkäranta On the stabilization of finite element approximations of the Stokes equations W. Hackbusch Efficient Solution of Elliptic Systems 1984 Vieweg
9. E. Burman P. Hansbo Edge stabilization for Galerkin approximations of convection-diffusion problems Comput. Methods Appl. Mech. Engrg. 193 2004 1437-1453
10. E. Burman, M. Fernàndez, P. Hansbo, Edge stabilization for the incompressible Navier-Stokes equations: A continuous interior penalty method, PREPRINT EPFL 23.2004.
11. P. Clément Approximation by finite element functions using local regularization RAIRO Anal. Numer. 9 R-2 1975 77-84
12. R. Codina J. Blasco Analysis of a pressure-stabilized finite element approximation of the stationary Navier-Stokes equations Numer. Math. 8 2000 59-81
13. C. Dohrmann P. Bochev A stabilized finite element method for the Stokes problem based on polynomial pressure projections Int. J. Numer. Methods Fluids 46 2004 183-201
14. J. Douglas J.P. Wang An absolutely stabilized finite-element method for the Stokes problem Math. Comp. 52 1989 495-508
15. J.J. Droux T.J.R. Hughes A boundary integral modification of the Galerkin least-squares formulation for the Stokes problem Comput. Methods Appl. Mech. Engrg. 113 1994 173-182
16. L.P. Franca A. Russo Approximation of the Stokes problem by residual-free macro bubbles East-West J. Numer. Math. 4 4 1996 265-278
17. V. Girault P.-A. Raviart Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms 1986 Springer-Verlag Berlin
18. T.J.R. Hughes L.P. Franca M. Balestra A new finite element formulation for computational fluid dynamics. V. Circumventing the Babuška-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accomodating equal-order interpolations Comput. Methods Appl. Mech. Engrg. 59 1986 85-99
19. K.A. Mardal X.C. Tai R. Winther A robust finite element method for Darcy-Stokes flow SIAM J. Numer. Anal. 40 2002 1605-1631
20. A. Masud T.J.R. Hughes A stabilized mixed finite element method for Darcy flow Comput. Methods Appl. Mech. Engrg. 191 2002 4341-4370
21. S. Norburn D. Silvester Stabilised vs stable mixed methods for incompressible flow Comput. Methods Appl. Mech. Engrg. 166 1998 131-141
22. D. Silvester Optimal low order finite element methods for incompressible flow Comput. Methods Appl. Mech. Engrg. 111 1994 357-368
23. V. Thomée Galerkin Finite Element Methods for Parabolic Problems 1984 Springer-Verlag Berlin