A stable nonconforming quadrilateral finite element method for the stationary Stokes and Navier-Stokes equations

Calcolo

Volumn 36, Issue 4, 1999, Pages 215-232

  Cai, Zhiqiang ^a   Douglas, Jim ^a   Ye, Xiu ^b  

^a PURDUE UNIVERSITY   (United States)

^b University of Arkansas   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE ELEMENT METHOD; NAVIER STOKES EQUATIONS;

A-STABLE; ELLIPTIC EQUATIONS; LOW ORDER; OPTIMAL ERROR ESTIMATE; PIECE-WISE CONSTANTS; QUADRILATERAL FINITE ELEMENT; STABLE ELEMENTS;

VISCOUS FLOW;

EID: 0001294328     PISSN: 00080624     EISSN: None     Source Type: Journal    
DOI: 10.1007/s100920050031     Document Type: Article

References (10)

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3. Crouzeix, M., Raviart, P.A.: Conforming and nonconforming finite element methods for solving the stationary Stokes equations. I. Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge 7, 33-76 (1973)
4. Douglas, J., Jr., Santos, J.E., Sheen, D., Ye, X.: Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems. RAIRO Modél. Math. Anal. Numér., to appear
5. Girault, V., Raviart, P.A.: Finite element methods for Navier-Stokes equations. Theory and algorithms. Berlin: Springer 1986
6. Han, H.-D.: Nonconforming elements in the mixed finite element method. J. Comput. Math. 2, 223-233 (1984)
7. Kellogg, R.B., Osborn, J.E.: A regularity result for the Stokes problem in a convex polygon. J. Funct. Anal. 21, 397-431 (1976)
8. Ladyzhenskaya, O.A.: The mathematical theory of viscous incompressible flow. New York: Gordon and Breach 1963
9. Rannacher, R., Turek, S.: Simple nonconforming quadrilateral Stokes element. Numer. Methods Partial Differential Equations 8, 97-111 (1992)
10. Zine, A.: Méthodes hybrides pour les éléments finis non conformes, "Résolution d'un système de Stokes". Thèse, Univ. Paris 1984