Finite-element error estimates for the MAC scheme

IMA Journal of Numerical Analysis

Volumn 16, Issue 3, 1996, Pages 347-379

  Girault, V ^a   Lopez, H ^b  

^a CNRS   (France)

^b FACULTAD DE CIENCIAS   (Venezuela)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENCE EQUATIONS; ERRORS; ESTIMATION; NAVIER STOKES EQUATIONS;

ERROR ESTIMATES; FINITE-ELEMENT APPROACH; INCOMPRESSIBLE NAVIER STOKES EQUATIONS; MATHEMATICAL THEORY; MIXED FINITE ELEMENT METHODS; QUADRATURE FORMULA; RECTANGULAR GRIDS; THREE-DIMENSIONAL PROBLEMS;

FINITE ELEMENT METHOD;

EID: 0041113622     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/16.3.347     Document Type: Article

References (25)

1. ADAMS, R. 1975 Sobolev Spaces. New York: Academic.
2. AUBIN, J.-P. 1967 Behavior of the error of the approximate solutions of boundary value problems for linear elliptic operators by Galerkin's and finite difference methods. Ann. Scuola Sup. Pisa 21, 599-637.
3. BERNARDI, C., GIRAULT, V., & MADAY, Y. 1992 Mixed spectral element approximation of the Navier-Stokes equations in the stream-function and vorticity formulation. IMA J. Numer. Anal. 12, 565-608.
4. BRENNER, S., & SCOTT, R. 1994 The Mathematical Theory of Finite Element Methods (Springer Texts in Applied Mathematics 15). Berlin: Springer.
5. CHOUDHURY, S., & NICOLAIDES, R. A. 1991 Discretization of incompressible vorticity-velocity equations on triangular meshes. Int. J. Numer. Methods Fluid Dyn. 11.
6. CIARLET, P. G. 1977 The Finite Element Method for Elliptic Problems. Amsterdam: North-Holland.
7. CLÉMENT, P. 1975 Approximation by finite-element functions using local regularization. RAIRO Anal. Numér. 9 R2, 77-84.
8. DALY, B. J., HARLOW, F. H., SHANNON, J. P. & WELCH, J. E. 1965 The MAC method. Technical Report LA-3425, Los Alamos Scientific Laboratory, University of California.
9. GIRAULT, V. 1995 A local projection operator for quadrilateral finite elements. Math. Comput. 64, 1421-1431.
10. GIRAULT, V., & RAVIART, P.-A. 1979 An analysis of a mixed finite element method for the Navier-Stokes equations. Numer. Math. 33, 235-271.
11. GIRAULT, V., & RAVIART, P.-A. 1986 Finite Element Methods for Navier-Stokes Equations. Theory and Algorithms (SCM 5). Berlin: Springer.
12. GRISVARD, P. 1985 Elliptic Problems in Nonsmooth Domains (Pitman Monographs and Studies in Mathematics 24). London: Pitman.
13. LEBEDEV, V. I. 1964 Difference analogues of orthogonal decompositions, fundamental differential operators and certain boundary-value problems of mathematical physics. Z. Vycisl. Mat. Mat. Fiz. 4, 449-465. (In Russian.)
14. LIONS, J.-L. 1969 Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires. Paris: Gauthier-Villars.
15. Nečas, J. 1967 Les Méthodes Directes en Théorie des Eq́uations Elliptiques. Paris: Masson.
16. NICOLAIDES, R. A. 1992 Analysis and convergence of the MAC scheme. The linear problem. SIAM J. Numer. Anal. 29, 1579-1591.
17. NICOLAIDES, R. A., & WU, X. 1993 Analysis and convergence of the MAC scheme. Navier-Stokes equations. Preprint.
18. NITSCHE, J. 1968 Ein kriterium fur die quasi-optimalitat des Ritzchen Verfahrens. Numer. Math. 11, 346-348.
19. RAUGEL, G. 1978 Résolution numérique de problèmes elliptiques dans des domaines à coins. Thèse de 3ème Cycle, Université de Rennes.
20. RANNACHER, R., & TUREK, S. 1992 Simple nonconforming quadrilateral Stokes element. Numer. Methods Partial Diff. Equations 8, 97-111.
21. SCHOLZ, R. 1978 A mixed method for fourth order problems using linear finite elements. RAIRO Anal. Numér. 12, 85-90.
22. TARTAR, L. 1978 Topics in Nonlinear Analysis. Université de Paris-Sud: Publications Mathématiques d'Orsay.
23. TEMAM, R. 1977 Theory and Numerical Analysis of the Navier-Stokes Equations. Amsterdam: North-Holland.
24. THOMAS, J.-M. 1977 Sur l'analyse numérique des méthodes d'éléments finis hybrides et mixtes. Thèse, Université Pierre et Marie Curie.
25. WAHLBIN, L. B. 1978 Maximum norm error estimates in the finite element method with isoparametric quadratic elements and numerical integration. RAIRO Anal. Numér. 12, 173-202.