A quasi-local interpolation operator preserving the discrete divergence

Calcolo

Volumn 40, Issue 1, 2003, Pages 1-19

  Girault, V ^a   Scott, L R ^b  

^a UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

^b UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION PROPERTIES; FLUID MODELING; INCOMPRESSIBLE FLUID; INF-SUP CONDITIONS; INTERPOLANTS; INTERPOLATION OPERATOR; LOCAL APPROXIMATION; LOCAL INTERPOLATION; LOW DEGREE; NONCONFORMING ELEMENT;

INTERPOLATION;

EID: 0037595549     PISSN: 00080624     EISSN: None     Source Type: Journal    
DOI: 10.1007/s100920300000     Document Type: Article

References (27)

1. Adams, R.A.: Sobolev spaces. New York: Academic Press 1975
2. Arnold, D., Brezzi, F., Fortin, M.: A stable finite-element for the Stokes equations. Calcolo 21, 337-344 (1984)
3. Bercovier, M., Pironneau, O.: Error estimates for finite-element method solution of the Stokes problem in the primitive variables. Numer. Math. 33, 211-224 (1979)
4. Bernardi, C.: Optimal finite element interpolation on curved domains. SIAM J. Numer. Anal. 26, 1212-1240 (1989)
5. Bernardi, C., Raugel, G.: Analysis of some finite elements for the Stokes problem. Math. Comp. 44, 71-79 (1985)
6. Boland, J., Nicolaides, R.: Stability of finite elements under divergence constraints. SIAM J. Numer. Anal. 20, 722-731 (1983)
7. Boffi, D.: Stability of higher order triangular Hood-Taylor methods for the stationary Stokes equations. Math. Models Methods Appl. Sci. 4, 223-235 (1994)
8. Boffi, D.: Three-dimensional finite element methods for the Stokes problem. SIAM J. Numer. Anal. 34, 664-670 (1997)
9. Brezzi, F., Falk, R.S.: Stability of higher-order Hood-Taylor methods. SIAM J. Numer. Anal. 28, 581-590 (1991)
10. Brezzi, F., Fortin, M.: Mixed and hybrid finite element methods. New York: Springer 1991
11. Ciarlet, P.G.: Basic error estimates for elliptic problems. In: Ciarlet, P.G., Lions, J.-L. (eds.): Handbook of numerical analysis. Vol. II. Finite element methods. Part 1. Amsterdam: North-Holland 1991, pp. 17-351
12. Crouzeix, M., Falk, R.S.: Nonconforming finite elements for the Stokes problem. Math. Comp. 52, 437-456 (1989)
13. Crouzeix, M., Raviart, P.-A.: Conforming and nonconforming finite element methods for solving the stationary Stokes. I. Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge 7, 33-75 (1973)
14. Fortin, M.: An analysis of the convergence of mixed finite element methods. RAIRO Anal. Numer. 11, 341-354 (1977)
15. Fortin, M., Soulié, M.: A nonconforming piecewise quadratic finite element on triangles. Internat. J. Numer. Methods Engrg. 19, 505-520 (1983)
16. Girault, V., Lions, J.-L.: Two-grid finite-element schemes for the steady Navier-Stokes problem in polyhedra. Port. Math. (N.S.) 58, 25-57 (2001)
17. Girault, V., Raviart, P.-A.: Finite element methods for Navier-Stokes equations. Theory and algorithms. Berlin: Springer 1986
18. Girault, V., Scott, L.R.: Finite-element discretizations of a two-dimensional grade-two fluid model. M2AN Math. Model. Numer. Anal. 35, 1007-1053 (2001)
19. Girault, V., Scott, L.R.: Upwind discretizations of a steady grade-two fluid model in two dimensions. In: Cioranescu, D., Lions, J.-L. (eds.): Nonlinear partial differential equations and their applications. College de France Seminar. Vol. XIV. Amsterdam: Elsevier 2002, pp. 393-414
20. Grisvard, P.: Elliptic problems in nonsmooth domains. (Monographs and Studies in Mathematics 24) Boston: Pitman 1985
21. Hood, P., Taylor, C.: A numerical solution of the Navier-Stokes equations using the finite element technique. Internat. J. Comput. & Fluids 1, 73-100 (1973)
22. Lions, J.-L., Magenes, E.: Problèmes aux limites non homogènes et applications. I. Paris: Dunod 1968
23. Mansfield, L.: Finite element subspaces with optimal rates of convergence for the stationary Stokes problem. RAIRO Anal. Numér. 16, 49-66 (1982)
24. Nečas, J.: Les méthodes directes en théorie des équations elliptiques. Paris: Masson 1967
25. Scott, L.R., Zhang, S.: Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comp. 54, 483-493 (1990)
26. Stenberg, R.: Analysis of mixed finite element methods for the Stokes problem: a unified approach. Math. Comp. 42, 9-23 (1984)
27. Verfürth, R.: Error estimates for a mixed finite element approximation of the Stokes equations. RAIRO Anal. Numér. 18, 175-182 (1984)