@phdthesis{BJHTUP11_1992__0322__A1_0, author = {Pascal, Fr\'ed\'eric}, title = {M\'ethodes de {Galerkin} non lin\'eaires en discr\'etisation par \'el\'ements finis et pseudo-spectrale : application \`a la m\'ecanique des fluides}, series = {Th\`eses d'Orsay}, publisher = {Universit\'e de Paris-Sud Centre d'Orsay}, number = {322}, year = {1992}, language = {fr}, url = {http://archive.numdam.org/item/BJHTUP11_1992__0322__A1_0/} }
TY - BOOK AU - Pascal, Frédéric TI - Méthodes de Galerkin non linéaires en discrétisation par éléments finis et pseudo-spectrale : application à la mécanique des fluides T3 - Thèses d'Orsay PY - 1992 IS - 322 PB - Université de Paris-Sud Centre d'Orsay UR - http://archive.numdam.org/item/BJHTUP11_1992__0322__A1_0/ LA - fr ID - BJHTUP11_1992__0322__A1_0 ER -
%0 Book %A Pascal, Frédéric %T Méthodes de Galerkin non linéaires en discrétisation par éléments finis et pseudo-spectrale : application à la mécanique des fluides %S Thèses d'Orsay %D 1992 %N 322 %I Université de Paris-Sud Centre d'Orsay %U http://archive.numdam.org/item/BJHTUP11_1992__0322__A1_0/ %G fr %F BJHTUP11_1992__0322__A1_0
Pascal, Frédéric. Méthodes de Galerkin non linéaires en discrétisation par éléments finis et pseudo-spectrale : application à la mécanique des fluides. Thèses d'Orsay, no. 322 (1992), 242 p. http://numdam.org/item/BJHTUP11_1992__0322__A1_0/
[I.1] Le modèle de simulation numérique de turbulence bidimensionnelle du L.M.D., Note interne LMD114, 1982.
,[I.2] Modélisation des échelles virtuelles dans la simulation numérique des écoulements turbulents bidimensionnels J. de Mécanique théorique et appliquée, 1983, 243-269.
and ,[I.3] Ergodic properties of inviscid truncated models of 2 dimensioned incompressible flows, J. of Fluid Mechanics, 69, 673-688, 1975. | Zbl | DOI
and ,[I.4] On the dimension of the attractors in two-dimensional turbulence, Physica D 30, 284-296, 1988. | MR | Zbl
, et ,[I.5] Global Lyapunov exponents, Kaplan-Yorke formulas and dimension of attractors for two-dimensional Navier-Stokes equations Comm. Pure App. Math. 38, 1-27, 1985. | MR | Zbl
et ,[I.6] Solution of the incompressible Navier-Stokes equations by the nonlinear Galerkin method, to appear in J. of Comp. Phys. | MR | Zbl
, and ,[I.7] Structure of the set of stationary solutions of the Navier-Stokes equations, Comm. Pure Appl. Math. 30, 149-164, 1977. | MR | Zbl
et ,[I.8] Some analytic and geometric properties of the solutions of the Navier-Stokes equations, J. Math. Pure Appl. 58, 339-368, 1979. | MR | Zbl
et ,[I.9] Variétés inertielles des équations dififferentielles dissipatives C.R.A.S. I, 301, 139-142, 1985. | MR | Zbl
, et ,[I.10] On the interaction of small and large eddies in two-dimensional turbulent flows, Math. Mod. and Num. Anal.(M2AN), 22, 1988, 93-114. | MR | Zbl | Numdam
, and ,[I.11] Résolution numérique des équations de Navier-Stokes instationnaires par méthodes spectrales. Méthode de Galerkin nonlinéaire, Thèse Université de Paris-Sud, 1990.
,[I.12] The nonlinear Galerkin method in computational fluid dynamics, App. Num. Math. 6, 1989, 361-370. | MR | Zbl
, and ,[I.13] A Nonlinear Galerkin Method for Navier Stokes Equations, Comp. Meth. in App. Mec. and Eng. 80, 1990 , 245-260. | MR | Zbl
, and , :[I.14] Cascade inverse et dispersion turbulente en turbulence bidimensionnelle, Thèse de Doctorat de l'Ecole Nationale des Ponts et Chaussées, 1988.
,[I.15] Turbulence in fluids. Stochastic and numerical modelling, Klurver Academic Publishers, 2nd revised edition. | MR | Zbl
,[I.16] Nonlinear Galerkin Methods, SIAM J. Num. Anal., 26, 1989, 1139-1157. | MR | Zbl | DOI
and ,[I.17] Numerical simulation of incompressible flow within simple boundaries in Galerkin spectral representation, Studies in applied mathematics, 50, 1971, 239-327. | MR | Zbl
,[I.18] Time analyticity and gevrey regularity for solutions of a class of dissipative partial differential equations, Nonlinear Anal., Th., Met. et App., Vol. 16, No 11, pp 959-980, 1991. | MR | Zbl
,[I.19] Chaotic evolution and strange attractors, Academia nazionale dei Lincey, Cambridge University Press 89. | MR | Zbl
,[I.20] Une classe d'opérateurs adaptés à la modélisation de la diffusion turbulente en dimension deux, C.R.A.S., Série II, t. 292 (27 avril 1981). | MR | Zbl
and ,[I.21] Hopf bifurcation of the unsteady regularized driven cavity flow, J. of Comp. Phys., 95, 228-245, 1991. | Zbl | DOI
,[I.22] A nonlinear Galerkin method for the Navier-Stokes equations, Comp. Meth. in Appl. Mech. and Eng., 80, 245-260, 1990. | MR | Zbl
,[I.23] Etude numérique de la turbulence bidimensionnelle homogène et cisaillée, Thèse de Doctorat de l'institut National Polytechnique de Grenoble, 1985.
,[I.24] Navier-Stokes equations, Amsterdam, North Holland, 1984. | MR | Zbl
,[I.25] Variétés inertielles approximatives pour les équations de Navier-Stokes bidimensionnelles, C.R.A.S., Série II, t. 306, 1988, 399-402. | MR | Zbl
,[I.26] Inertial Manifolds The mathematical intelligencer vol 12, no 4, 1990. | MR | Zbl
,[I.27] Approximation of attractors, large eddies simulation and multiscale methods, Proc. of the Royal Society A, special issue commemorating the work of A.N. Kolmogorov, 1991. | MR | Zbl
,[I.28] On approximate inertial manifolds to the Navier-Stokes equations, J. of Math. Anal, and Appl., Vol. 149, No 2, 540-557, 1990. | MR | Zbl | DOI
,[1] Modélisation des échelles virtuelles dans la simulation numérique des écoulements turbulents bidimensionnels J. de Mécanique théorique et appliquée, 1983, 243-269.
and ,[2] Solution of the incompressible Navier-Stokes equations by the nonlinear Galerkin method, to appear in J. of Comp. Phys. | MR | Zbl
, and ,[3] On the interaction of small and large eddies in two-dimensional turbulent flows, Math. Mod. and Num. Anal. (M2AN), 22, 1988, 93-114. | MR | Zbl | Numdam
, and ,[4] Résolution numérique des équations de Navier-Stokes instationnaires par méthodes spectrales. Méthode de Galerkin nonlinéaire, Thèse Université de Paris-Sud, 1990.
,[5] The nonlinear Galerkin method in computational fluid dynamics, App. Num. Math. 6, 1989, 361-370. | MR | Zbl
, and ,[6] A Nonlinear Galerkin Method for Navier Stokes Equations, Comp. Meth. in App. Mec. and Eng. 80, 1990 , 245-260. | MR | Zbl
, and ,[7] Nonlinear Galerkin Methods, SIAM J. Num. Anal., 26, 1989, 1139-1157. | MR | Zbl | DOI
and ,[II.2] Numerical methods for non linear variational problems Springer Verlag, 1984. | MR
,[II.3] Navier-Stokes equations, Amsterdam, North Holland, 1984. | MR | Zbl
,[II.4] Implementation of finite element methods for Navier-Stokes equations, Springer Verlag, 1981. | MR | Zbl | DOI
,[II.6] A stable finite element for the Stokes equations, Calcolo 21(4), 337-344, 1984. | MR | Zbl
, and ,[II.7] Some fast 3-D finite element solvers for Generalized Stokes problem, Rapport EDF, HE/41/87.03, 1987. | MR | Zbl
et ,[II.8] Conforming and non conforming finite element methods for the stationnary Stokes equations, RAIRO, R3, 33-76, 1973. | MR | Zbl | Numdam
and ,[II.9] Calcul numérique des écoulements des fluides de Bingham et des fluides newtoniens incompressibles par la méthode des éléments finis, Thèse, Université Paris VI, 1972.
,[II.10] Navier-Stokes equations using mixed interpolation, in Finite element in flow problem, Oden ed., UAD Press, 1974.
and ,[II.11] Why finite elements ?, Finite Elements in Fluids, Vol 1, edited by Gallagher, Oden, Taylor, Zienkiewicz ; Wiley & Sons.
,[II.13] Error estimates for finite element solution of the Stokes problem in the primitive variables, Numer. Math. 33, 211-224, 1979. | MR | Zbl
and ,[II.14] On a mixed Finite element approximation of the Stokes problem, Numer. Math., 33, 397-424, 1979. | MR | Zbl
and ,[II.15] A mixed finite element approximation of the Navier-Stokes equation, Numer. Math. 35, 381-404, 1980. | MR | Zbl
,[II.17] On the numerical solution of non linear problems in fluid dynamics by least squares and finite element methods (1) least square formulations and conjugate gradient solution of the continuous problems, Comp. Meth. in appl. Mech. and Eng. 17/18, 619-657, 1979. | MR | Zbl
, , , and ,[II.19] Numerical solution of incompressible flow problems, Numerical Analysis, 2 , 64-71, 1968. | MR | Zbl
,[II.20] Numerical methods for nonlinear problem in fluid dynamics, Supercomputing, A. Lichnevsky, C. Saguez ed., North Holland, 1987. | MR | Zbl
et ,[II.21] Splitting algorithms for the sum of two nonlinear operator, SIAM J. Num. Anal. 16, 964-979, 1979. | MR | Zbl | DOI
, ,[II.22] Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires (I), Arch. Rational Mech. Anal. 32, 1969, p135-153 | MR | Zbl
,[II.23] Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires (II), Arch. Rational Mech. Anal. 33, 1969, p377-385 | MR | Zbl
,[II.25] An efficient scheme for solving steady incompressible Navier-Stokes equations, Jour, of Comp. Phys. 89, 389-413, 1990. | Zbl | DOI
, ,[II.26] High-Re Solutions for incompressible Flow using the Navier-Stokes equations and a multigrid method, J. of Comp. Phys. 48, 387- 411, 1982. | Zbl | DOI
, et ,[II.27] Hopf bifurcation in the driven cavity, Jour. of Comp. Phys. 90, 219-261, 1990. | MR | Zbl | DOI
, , ,[II.28] Hopf bifurcation of the unsteady regularized driven cavity flow, Jour, of Comp. Phys., 95, 228-245, 1991. | Zbl | DOI
,[II.29] Résolution numérique des équations de Stokes et Navier-Stokes par les méthodes spectrales, thèse de 3e cycle, Université de Paris-Sud, 1987.
,[II.30] Etude numérique des équations de Navier-Stokes en milieux multiplement connexes, en formulation vitesse-tourbillon, par une approche multidomaines, thèse de 3e cycle, Université de Paris-Sud, 1989.
,[III.1] The hierarchical basis multigrid method, Numer. Math. 52, 427-458, 1988. | MR | Zbl
, , ,[III.2] A multigrid tutorial, S.I.A.M., Philadelphia, Pennsylvania, 1987. | MR
,[III.3] Résolution numérique des grands systèmes linéaires, CEA-EDF-INRIA, Ecole d'été d'analyse numérique, 49, Eyrolles. | MR | Zbl
, ,[III.4] Nonlinear Galerkin method with finite element approximation, XII ICNMFD, Oxford, 1989. | MR
, , ,[III.5] Nonlinear Galerkin Methods, SIAM J. Num. Anal., 26, 1139-1157, 1989. | MR | Zbl | DOI
and ,[III.6] Nonlinear Galerkin Methods : the finite element case, Numer. Math. 57, 205-226, 1990. | MR | Zbl
and ,[III.7] Introduction à l'analyse numérique des équations aux dérivées partielles, Masson. | MR | Zbl
,[III.8] Iterative methods for the numerical solution of mixed finite element approximations of the Stokes problem, Rapport INRIA, 379, 1985.
,[III.9] Hierarchical bases give conjugate gradient type methods, a multigrid speed of convergence, Appl. Math, and Comp. 19, 347-358, 1986. | MR | Zbl
,[III.10] On the multilevel splitting of finite element spaces, Numer. Math. 49, 379-412, 1986. | MR | Zbl
,[III.11] Hierarchical finite element approaches, error estimates and adaptive refinement, The mathematics of finite elements and applications IV (J.R. Whiteman, ed.), Mafelap 1981, London, 1982. | MR | Zbl
, , , ,[IV.1] Generating exact solutions of the two-dimensional Burgers' equations, Inter. Jour, for Num. Met. in fluids, 3, 213-216, 1983. | Zbl | DOI
,[IV.2] A comparison of finite element and finite difference solutions of the one and two dimensional Burgers' equations. J.C.P. 51, 159-188, 1983. | MR | Zbl
,[IV.3] Nonlinear Galerkin methods using hierarchical almost- orthogonal finite element bases, soumis à J. of nonlinear Analysis, theory, methods and applications. | MR | Zbl
,[IV .4] Numerical solutions of coupled Burgers' equation Int. J. Nonlinear Mechanics, 13, 213-222, 1978. | Zbl | DOI
and ,[IV.5] Nonlinear Galerkin Methods : the finite element case, Numer. Math. 57, 205-226, 1990. | MR | Zbl
and ,