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Conforming and nonconforming finite element methods for solving the stationary Stokes equations. I. (English) Zbl 0302.65087


MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids

References:

[1] BAZELEY G. P., CHEUNG Y. K., IRONS B. M. et ZIENKIEWICZ O. C., Triangular elements in bending-conforming and nonconforming solutions, Proc. Conf. Matrix Methods in Structural Mechanics, Air Forces Inst. of Tech., Wright Patterson A. F. Base, Ohio, 1965.
[2] BOLLEY P. et CAMUS J., (to appear).
[3] BRAMBLE J. H. et HILBERT S. R., Estimations of linear functionals on Sobolev spaces with applications to Fourier transforms and spline interpolation, J. Numer. Anal., 7, 1970, 112-124. Zbl0201.07803 MR263214 · Zbl 0201.07803 · doi:10.1137/0707006
[4] CATTABRIGA L., Su un problema al contorno relativo al sistema di equazioni di Stokes. Rend. Sem. Mat. Padova, 1961, 1-33. Zbl0116.18002 · Zbl 0116.18002
[5] CIARLET P. G. et RAVIART P.-A., General Lagrange and Hermite interpolation in \(R^n\) with applications to finite element methods, Arch. Rat. Mech. Anal., 46, 1972, 177-199. Zbl0243.41004 MR336957 · Zbl 0243.41004 · doi:10.1007/BF00252458
[6] CIARLET P. G. et RAVIART P.-A., Interpolation theory over curved elements with applications to finite element methods, Computer Meth. Appl. Mech. Engin., 1, 1972, 217-249. Zbl0261.65079 MR375801 · Zbl 0261.65079 · doi:10.1016/0045-7825(72)90006-0
[7] CIARLET P. G. et RAVIART P.-A., The combined effect of curved boundaries and numerical integration in isoparametric finite element methods. The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (A. K. Aziz, ed.), 409-474, Academic Press, New-York, 1972. Zbl0262.65070 MR421108 · Zbl 0262.65070
[8] FORTIN M., Calcul numérique des écoulements des fluides de Bingham et des fluides newtoniens incompressibles par la méthode des éléments finis, Thèse, Université de Paris VI, 1972.
[9] FORTIN M., Résolution des équations des fluides incompressibles par la méthode des éléments finis (to appear in Proc. 3rd Int. Conf. on the Numerical Methods in Fluid Mechanics, Paris, July 3-7, 1972, Springer Verlag).
[10] IRONS B. M et RAZZAQUE A., Experience with the pach test for convergence of finite elements, The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (A. K. Aziz, ed.), 557-588, Academic Press, New-York, 1972. Zbl0279.65087 MR423839 · Zbl 0279.65087
[11] JAMET P. et RAVIART P.-A., Numerical Solution of the Stationary Navier-Stokes equations by finite element methods (to appear). Zbl0285.76007 · Zbl 0285.76007
[12] LADYZHENSKAYA O. A., The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, New-York, 1962. Zbl0121.42701 · Zbl 0121.42701
[13] LIONS J.-L., Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969. Zbl0189.40603 MR259693 · Zbl 0189.40603
[14] DE RHAM, Variétés différentiables, Hermann, Paris, 1960. Zbl0089.08105 · Zbl 0089.08105
[15] STRANG G. et FIX G., An Analysis of the Finite Element Method, Prentice Hall, New-York, 1973. Zbl0356.65096 · Zbl 0356.65096
[16] ZIENKIEWICZ O. C., The Finite Element Method in Engineering Science, Mc Graw Hill, London, 1971. Zbl0237.73071 · Zbl 0237.73071
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