The aim of this work is to present a new spectral method without spurious modes for the Stokes system in any space dimension. This method use only the pressure and the velocity values at the nodes of a Gauss-Lobatto grid as variables.
@phdthesis{BJHTUP11_1991__0281__P0_0, author = {Azaiez, Majdi}, title = {Calcul de la pression dans le probl\`eme de stokes pour des fluides visqueux incompressibles par une m\'ethode spectrale de collocation}, series = {Th\`eses d'Orsay}, publisher = {Universit\'e de Paris-Sud Centre d'Orsay}, number = {281}, year = {1991}, language = {fr}, url = {http://www.numdam.org/item/BJHTUP11_1991__0281__P0_0/} }
TY - BOOK AU - Azaiez, Majdi TI - Calcul de la pression dans le problème de stokes pour des fluides visqueux incompressibles par une méthode spectrale de collocation T3 - Thèses d'Orsay PY - 1991 IS - 281 PB - Université de Paris-Sud Centre d'Orsay UR - http://www.numdam.org/item/BJHTUP11_1991__0281__P0_0/ LA - fr ID - BJHTUP11_1991__0281__P0_0 ER -
%0 Book %A Azaiez, Majdi %T Calcul de la pression dans le problème de stokes pour des fluides visqueux incompressibles par une méthode spectrale de collocation %S Thèses d'Orsay %D 1991 %N 281 %I Université de Paris-Sud Centre d'Orsay %U http://www.numdam.org/item/BJHTUP11_1991__0281__P0_0/ %G fr %F BJHTUP11_1991__0281__P0_0
Azaiez, Majdi. Calcul de la pression dans le problème de stokes pour des fluides visqueux incompressibles par une méthode spectrale de collocation. Thèses d'Orsay, no. 281 (1991), 124 p. http://numdam.org/item/BJHTUP11_1991__0281__P0_0/
(A.S) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Gov. Printing Office, Washington D.C.) (1972). | Zbl
& .(Ad) Sobolev Spaces. Academic Press, (1975). | MR
.(Ax) Conjugate gradient type methods for unsymmetric and inconsistent systems of linear equations. Linear Algebra and its Application. 29, 1-16 (1980). | MR | Zbl | DOI
.(A.H.U) Studies in Nonlinear Programming. Standford University Press, Standford, (1958). | Zbl
, , & .(A.L.V) A pressure field pseudo spectral evaluation for 3-D numerical experiments in incompressible fluid dynamics. In Proceedings of the Eleventh International Conference on Numerical Methods in Fluid Dynamics, Springer Verlag, (1989). | DOI
, , & .(A.L1) A unique grid spectral collocation 3-D Stokes solver : numerical study of the pressure operator. Presented in ICOSA-HOM 89, JUNE 26-29, 1989, COMO (Italy).
& .(A.L2) A multidimensional periodic-nonperiodic steady Stokes solver for primitive variables by spectral collocation method, submitted to jour. of Comp. Phys.
& .(B.al) Spectral and finite difference solutions of the Burgers equation. Comput. Fluids, (1986) 14, 23-41. | Zbl | DOI
, , , , , , & .(B.C.M) Generalized Inf-Sup condition 106 for Chebyshev approximation of the Stokes problem, SIAM J. Numer. Anal. 25 (1988), p. 1237-1271. | MR | Zbl | DOI
, & .(B.C.M.M) Single grid spectral collocation for the Navier-Stokes equations, à paraître dans I.M.A. Journal Numer. Anal. | MR | Zbl
, , & .(B.M.M.1) Calcul de la pression dans la résolution spectral du problème de Stokes. Recherche Aérospatiale 1 (1987), p. 1-21. | Zbl
, , & .(B.M.M.2) Spectral approximation of the periodic-nonperiodic Navier-Stokes equations. Numer. Math., 51 : 655-700, (1987). | MR | Zbl | DOI
, , & .(B.M.1) A collocation methods over staggred grids for the Stokes problem, Intern. J. for Num. Methods in Fluids, 8 (1988), p. 537-557. | MR | Zbl | DOI
& .(B.M.2) Relèvement polynômial de trace et applications, à paraître dans Modél. Math. et Anal. Numér. | MR | Numdam
& .(B.M.3) Properties of some weighted Sobolev spaces and application to spectral approximations, SIAM J. Numer. Anal. 26 (1989), p. 769-829. | MR | Zbl | DOI
& .(Bu) The non linear Diffusion Equation. D. Reidel Publisching Compagy, Dordrecht, Holland, (1974). | Zbl
.(Br) On the existence, uniqueness and approximation of saddle point problems arising from Lagrange multipliers. RAIRO Anal. Numer., 8 R2 : 129-151, (1974). | MR | Zbl | Numdam
.(C.Ch) Some fast 3-D finite element solvers for the generalized Stokes problem. Int. J. Meth. in Fluids, 8 : 869-895, (1988). | MR | Zbl | DOI
& .(C) Numerical solution of incompressible flow problems. In J.M. Ortega and W.C Rheinboldt, editors, Studies in Numerical Analysis 2, SIAM, (1970). | Zbl
.(C.H.Q.Z) Spectral Methods in Fluid Dynamics. Berlin : Springer-Verlag, (1987). | MR | Zbl
, , & .(C.Q) Approximation results for orthogonal polynomials in Sobolev Spaces ; Math. Comp, (1982) 67-86. | MR | Zbl | DOI
& .(D.R) Methods of Numerical Integration. Academic Press, (1985). | MR | Zbl
& .(F.P) Calculation of non-boussinesq convection by a pseudospectral method. Presented in ICOSAHOM 89, JUNE 26-29, 1989, COMO (Italy). | MR | Zbl
& .(G.R) Finite Element Approximation of the Navier Stokes Equations. Springer-Verlag, Berin, Heidelberg, (1986). | Zbl
& .(G) Numerical Methods for Nonlinear Variational Problems. Springer-Verlag,(1984). | MR | Zbl | DOI
.(G.P) On a mixed finite element approximation of the Stokes problem. Numer. Math., 33 : 397, (1979). | MR | Zbl
& .(G.O) Numerical and Analysis of Spectral Methods. SIAM, (1977). | MR | Zbl
& .(H) Résolution tridimensionelle des équations de Navier-Stokes par méthodes Spectrales Tchebycheff : Application a la convection naturelle, Thèse, Université de Provence, (1984).
.(H.L.D.A) Chebychev 3-D and 2-D pseudo spectral solver for the Helmholtz equation. J. Comp. Phy, 55 (1984). | MR | Zbl | DOI
, , & .(K.M) Application of a fractional-step method to incompressible Navier-Stokes equations. J. Comput. Phys., 59 : 309, (1985). | MR | Zbl
& .(Le) Mono and multi domain Chebyshev algorithm on staggered grid. In Proceedings of the Seventh International Conference on Finite Element Methods in Flow Problems,(1989).
.(Ma1) Analysis of spectral projectors in one dimensional domains, submitted to jour. of Comp. Phys. | MR | Zbl
.(M.M.A.L) Numerical and experimental study of multicellular free convection flows in an annular porous layer (à paraitre). | Zbl
, , , & .(M.M.P.R) Analysis of iterative methods for the steady and unsteady Stokes Problem : application to spectral element discretisation. Submitted to Journal of Computation Physics. | MR | Zbl
, , , & .(M.P.R) A well-posed optimal spectral element approximation for the Stokes problem. SIAM J. Numer. Anal., to appear.
. , & .(M.Q) Legendre and Chebychev spectral approximation of Burgers equation. Numer. Math., 37 (1981), pp. 321.332. | MR | Zbl | DOI
& .(Me) Résolution des équations de Navier-Stokes par méthodes spectrales. Thèse, Université Pierre-et-Marie-Curie, (1987).
.(Me.Mo) Une méthode spectrale avec prise en compte de la condition Inf-Sup pour le calcul d'un écoulement de fluide visqueux incompressible. La Recherche Aerospatiale.
& .(Pe) Introduction to Spectral Methods. Von Karman Institute Lecture Series 1986-04, Rhode-Saint Genese, Belgium. (1986)
.(SJ) Résolution numérique des équations de Stokes et de Navier-Stokes par les méthodes spectrales, Thèse, Université Paris Sud (1987).
.(T) Navier-Stokes Equations. Theory and Numerical Analysis. North-Holland, Amsterdam, (1977). | MR | Zbl
.(V1) Analysis of the eigenvalues of spectral differentiation operators. SIAM J. Numer. Anal., submitted.
.(V2) Compatibilité des espaces discrets pour l'approximation spectrale du problème de Stokes periodique non periodique.M2AM | Zbl | Numdam | DOI
.(Y.C.B) Multiple bouyancy-driven flows in a vertical cylinder heated from below. Phil. Trans. Roy. Soc. London, A 313 : 519, (1984). | MR | Zbl
, , & .(Z.H) Fourier-Legendre spectral methods for incompressible chanel flows, Proc. 9th. Conf. on Numer. Methods in Fluid Dynamics, Saclay (1984).
& .(1) - Nuacrical unulysis of spectral methods : theory and applications." SIAM, Philadephia. | MR | Zbl
, (1977) "(2) - The accurate solution of Poisson's equation by expansion in Chebychev polynomials.", J. Comp. Phys. 30. 167-180 | MR | Zbl | DOI
, (1979), "-Chebyshev 3-D spectral and 2-D pseudospectral solvers for the Helmholtz equation." J. Comp. Phys., 55, 115-128. | MR | Zbl | DOI
. , , (1984), "(3) - Calcul de la pression dans la résolution spectrale du problème de Stokes." La Recherche Aérospatiale, n° 1987-1. 1-21. | Zbl
, , (1987). "(4) - Résolution tridimensionnelle des équations de Navier-Stokes par methodes spectrales Tchebycheff : application à la convection naturelle." Ph.D.Thèse, Université de Provence.
(1984). "-
, (1986), proceedings of the 6th Int.Symp. on Finite Element Methods in Flow Problems. ed. by M.O. Bristeau, R. Clovinski, A. Hausel, J. Periaux, 261-266(5) - Conjugate gradient type methods for unsymetric and inconsistent systems of linear equations." Linear algebra and its applications, 29, 1-16 | MR | Zbl | DOI
(1980), "(6) - On the existence uniqueness and approximation of saddle-point problems arising from Lagrange multipliers.", RAIRO Anal. Numer. 8/R2. 129-151. | MR | Zbl | Numdam
(1974), "