Pressure projection stabilizations for Galerkin approximations of Stokes' and Darcy's proble

Numerical Methods for Partial Differential Equations

Volumn 24, Issue 1, 2008, Pages 127-143

  Burman, Erik ^a  

^a EPFL   (Switzerland)

Author keywords

Finite element methods; inf sup condition; Pressure stabilization; Stokes' problem

Indexed keywords

EID: 38049121233     PISSN: 0749159X     EISSN: 10982426     Source Type: Journal    
DOI: 10.1002/num.20243     Document Type: Article

References (19)

1. 1 D. Silvester, Optimal low order finite element methods for incompressible flow, Comput Methods Appl Mech Engrg 111 ( 1994), 357–368.
2. 2 R. Becker and M. Braack, A finite element pressure gradient stabilization for the Stokes equations based on local projections, Calcolo 38 ( 2001), 173–199.
3. 3 F. Brezzi and M. Fortin, A minimal stabilisation procedure for mixed finite element methods, Numer Math 89 ( 2001), 457–491.
4. 4 F. Brezzi and J. Pitkäranta, On the stabilization of finite element approximations of the Stokes equations, In Proceedings on the Efficient solutions of elliptic systems, Kiel, 1984, Notes on numerical fluid mechanics, Vol. 10, Vieweg, Braunschweig, 1984, pp. 11.
5. 5 C. R. Dohrmann and P. B. Bochev, A stabilized finite element method for the Stokes problem based on polynomial pressure projections, Internat J Numer Methods Fluids 46 ( 2004), 183–201.
6. 6 W. Layton, Model reduction by constraints, discretization of flow problems and an induced pressure stabilization, Numer Linear Algebra Appl 12 ( 2005), 547–562.
7. 7 K. Nasserdine and D. Silvester, Analysis of locally stabilized mixed finite element methods for the Stokes problem, Math Comp 58 ( 1992), 1–10.
8. 8 F. Brezzi, On the existence, uniqueness and approximation of saddle‐point problems arising from Lagrangian multipliers, Rev Française Automat Informat Recherche Opérationnelle Sér. Rouge 8 (R‐2) ( 1974), 129–151.
9. 9 M. Fortin, An analysis of the convergence of mixed finite element methods, RAIRO Anal Numér 11 ( 1977), 341–354, iii.
10. 10 V. Girault and P.‐A. Raviart, Finite element methods for Navier‐Stokes equations, Springer series in computational mathematics, Vol. 5, Springer‐Verlag, Berlin, 1986.
11. 11 L. R. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions, Math Comp 54 ( 1990), 483–493.
12. 12 R. Pierre, Regularization procedures of mixed finite element approximations of the Stokes problem, Numer Methods Partial Differential Equations 5 ( 1989), 241–258.
13. 13 E. Burman and P. Hansbo, Edge stabilization for the generalized Stokes problem: a continuous interior penalty method, Comput Methods Appl Mech Eng 195 ( 2006), 2393–2410.
14. 14 M. Bercovier and O. Pironneau, Error estimates for finite element method solution of the Stokes problem in the primitive variables, Numer Math 33 ( 1979), 211–224.
15. 15 N. Parolini and E. Burman, Subgrid edge stabilization for transport operators, Technical Report 9, EPFL/IACS, Lausanne, 2005.
16. 16 F. Brezzi and M. Fortin, Mixed and hybrid finite element methods, Springer series in computational mathematics, Vol. 15, Springer‐Verlag, New York, 1991.
17. 17 E. Burman, M. A. Fernández, and P. Hansbo, Continuous interior penalty finite element method for Oseen's equations, SIAM J Numer Anal 44 ( 2006), 1248–1274.
18. 18 F. Hecht and O. Pironneau, FEM++ manual, Laboratoire Jacques Louis Lions, France, 2005.
19. 19 A. Masud and T. J. R. Hughes, A stabilized mixed finite element method for Darcy flow, Comput Methods Appl Mech Eng 191 ( 2002), 4341–4370.