A stream-function-vorticity variational formulation for the exterior Stokes problem in weighted Sobolev spaces
作者： V. Girault , J. Giroire , A. Sequeira
关键词: Vector potential 、 Stream function 、 Sobolev space 、 Vorticity 、 Calculus of variations 、 Mathematical analysis 、 Mathematics 、 Domain (mathematical analysis) 、 Structure (category theory) 、 Bounded function 、 General Engineering 、 General Mathematics
摘要: In this paper we derive a mixed variational formulation for the exterior Stokes problem in terms of vorticity and stream function, or vector potential three dimensions. The main steps are construction function (or potential) proof Babuska–Brezzi ‘inf-sup’ condition. two- three-dimensional cases treated separately because structure differs substantially according to number dimensions considered. conclusion work is that if set weighted Sobolev spaces Hanouzet Giroire, analysis quite same as domain were bounded.
harvard.edu
sci-hub.se 参考文章(23)
J. C. N�d�lec, Éléments finis mixtes incompressibles pour l'équation de Stokes dans ℝ3 Numerische Mathematik. ,vol. 39, pp. 97- 112 ,(1982) , 10.1007/BF01399314
Vivette Girault, Pierre-Arnaud Raviart, Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms ,(1986)
R. Glowinski, O. Pironneau, Numerical methods for the first biharmonic equation and for the two-dimensional Stokes problem Siam Review. ,vol. 12, pp. 167- 212 ,(1977) , 10.1137/1021028
Georges H. Guirguis, On the existence, uniqueness and regularity of the exterior stokes problem in R3 Communications in Partial Differential Equations. ,vol. 11, pp. 567- 594 ,(1986) , 10.1080/03605308608820437
Vivette Girault, Adelia Sequeira, A well-posed problem for the exterior Stokes equations in two and three dimensions Archive for Rational Mechanics and Analysis. ,vol. 114, pp. 313- 333 ,(1991) , 10.1007/BF00376137
CHRISTINE BERNARDI, VIVETTE GIRAULT, YVON MADAY, Mixed spectral element approximation of the Navier-Stokes equations in the stream-function and vorticity formulation Ima Journal of Numerical Analysis. ,vol. 12, pp. 565- 608 ,(1992) , 10.1093/IMANUM/12.4.565
Peter Monk, A Mixed Finite Element Method for the Biharmonic Equation Mathematical Aspects of Finite Elements in Partial Differential Equations#R##N#Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin–Madison, April 1–3, 1974. pp. 125- 145 ,(1974) , 10.1016/B978-0-12-208350-1.50009-1
V. Girault, P. A. Raviart, An analysis of a mixed finite element method for the Navier-Stokes equations Numerische Mathematik. ,vol. 33, pp. 235- 271 ,(1979) , 10.1007/BF01398643
Robert Finn, On the exterior stationary problem for the navier-stokes equations, and associated perturbation problems Archive for Rational Mechanics and Analysis. ,vol. 19, pp. 363- 406 ,(1965) , 10.1007/BF00253485
Robert C. McOwen, The behavior of the laplacian on weighted sobolev spaces Communications on Pure and Applied Mathematics. ,vol. 32, pp. 783- 795 ,(1979) , 10.1002/CPA.3160320604