Navier-stokes equations: Theory and approximation

Handbook of Numerical Analysis

Volumn 6, Issue , 1998, Pages 503-689

  Marion, Martine ^a   Temam, Roger ^b  

^a Département Mathématiques   (France)

^b UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000122159     PISSN: 15708659     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1570-8659(98)80010-0     Document Type: Review

References (203)

1. Abergel F., and Temam R. On some control problems in fluid mechanics. Theoret. Comput. Fluid Dynamics 1 (1990) 303-325
2. Adams R.A. Sobolev Spaces (1975), Academic Press, London
3. Ait Ou Ammi A. Thesis (1994), Ecole Centrale de Lyon, New York, San Francisco, London
4. Ait Ou Ammi A., and Marion M. Nonlinear Galerkin methods and mixed finite elements: two-grid algorithms for the Navier-Stokes equations. Numer. Math. 68 (1994) 189-213
5. Ait Ou Ammi A., Marion M., and Zine M. Schémas à deux niveaux pour les problèmes mixtes. C.R. Acad. Sci. Paris Série I 321 (1995) 487-490
6. Arrow K., Hurwicz L., and Uzawa H. Studies in Nonlinear Programming (1968), Stanford University Press
7. Axelsson O., and Varker V.A. Finite Element Solution of Boundary Value Problems (1984), Academic Press, Stanford
8. (in Russian). Russian Math. Surveys 38, 151-213 (in English). Babin A.V., and Vishik M.I. Attractors of partial differential equations and estimate of their dimension. Uspekhi Mat. Nauk 38 (1983) 133-187
9. Babin A.V., and Vishik M.I. Attractors of Evolution Equations (1992), North-Holland, Orlando
10. Preprint. Bartuccelli M., Doering C., and Gibbon J.D. Ladder theorems for the 2D and 3D Navier-Stokes equations on a finite periodic domain (1990)
11. Batchelor G.K. The Theory of Homogeneous Turbulence (1970), Cambridge University Press, Amsterdam
12. Batchelor G.K. An Introduction to Fluid Dynamics (1988), Cambridge University Press, Cambridge
13. Beale J.T., and Greengard C. Convergence of Euler-Stokes splitting of the Navier-Stokes equations. Comm. Pure Appl. Math. 47 8 (1994) 1083-1115
14. Beale J.T., Kato T., and Majda A. Remarks on the breakdown of smooth solutions for the 3D Euler equations. Comm. Math. Phys. 94 (1984) 61-66
15. Bell J., Colella P., and Glaz H. A second-order projection method for the incompressible Navier-Stokes equations. J. Comput. Phys. 85 (1989) 257-283
16. Bernardi C., and Maday Y. Approximations Spectrales de Problèmes aux Limites Elliptiques (1992), Springer, Cambridge
17. Bernardi C., and Maday Y. Spectral methods. In: Ciarlet P.G., and Lions J.L. (Eds). Handbook of Numerical Analysis V (1996), North-Holland, Paris 209-485
18. Bernardi C., and Raugel G. A conforming finite element method for the time-dependent Navier-Stokes equations. SIAM J. Numer. Anal. 22 (1985) 455-473
19. July 11, 1996, San Diego, Book No. H01073. Bewley T., Moin P., and Temam R. A method for optimizing feedback control rules for wall-bounded turbulent flows based on control theory. Proc. ASME Fluid Mechanics Conference FED 237 (1996)
20. Bewley T., Moin P., and Temam R. Optimal and robust approaches for linear and nonlinear regulation problems in fluid mechanics. AIAA 97-1872, 28th AIAA Fluid Dynamics Conference and 4th AIAA Shear Flow Control Conference (1997), American Institute of Aeronautics and Astronautics, Amsterdam
21. to appear. Bewley T., Moin P., and Temam R. Control of turbulent flows. Proc. of the 18th IFIP TC7 Conference on System Modelling and Optimization. Detroit, MI, July 1997 (1997)
22. Bréfort B., Ghidaglia J.M., and Temam R. Attractors for the penalized Navier-Stokes equations. SIAM J. Math. Anal. 19 (1988) 1-21
23. Brezis H., and Gallouet T. Nonlinear Schrödinger evolution equation. Nonlinear Anal. 4 (1980) 667-681
24. Brezzi F., and Fortin M. Mixed and Hybrid Finite Element Methods (1991), Springer
25. Bruneau C.H., and Fabrie P. Effective downstream boundary conditions for incompressible Navier-Stokes equations. Internat. J. Numer. Methods Fluids 19 (1994)
26. Bruneau C.H., and Fabrie P. Computation of incompressible flows and direct simulation of the transition to turbulence. Proc. of the 14th ICNMFD. Lecture Notes in Physics 453 (1995), Springer, New York
27. Bruneau C.H., and Fabrie P. New efficient boundary conditions for incompressible Navier-Stokes equations: a well-posedness result. Math. Model. and Numer. Anal. (M2AN) 30 7 (1996) 815-840
28. Bruneau C.H., and Jouron C. An efficient scheme for solving steady incompressible Navier-Stokes equations. J. Comput. Phys. 89 (1990) 2
29. Preprint 175. Burie J., and Marion M. Multi-level methods in space and time for the Navier-Stokes equations, Equipe d'Analyse Numérique Lyon-Saint-Etienne. to appear. SIAM J. Numer. Anal. 34 (1997)
30. Caffarelli L., Kohn R., and Nirenberg L. Partial regularity of suitable weak solutions of the Navier-Stokes equations. Comm. Pure Appl. Math. 35 (1982) 771-831
31. Calgaro C., Laminie J., and Temam R. A dynamical multilevel scheme for the solution of evolution equations by hierarchical finite element discretization. Appl. Numer. Math. 21 (1997) 1-40
32. Canuto C., Hussaini M.Y., Quarteroni A., and Zang T.A. Spectral Methods in Fluid Dynamics (1987), Springer, New York
33. Céa J. Approximation variationnelle des problèmes aux limites. Ann. Inst. Fourier (Grenoble) 14 (1964) 345-444
34. Chehab J.P., and Temam R. Incremental unknowns for solving nonlinear eigenvalue problems: new multiresolution methods. Numerical Methods Partial Differential Equations 11 3 (1995) 199-228
35. Chen M., Miranville A., and Temam R. Incremental unknowns in finite differences in space dimension three. Matematica Aplicada e Computacional 14 3 (1995) 219-252
36. Chen M., and Temam R. Incremental unknowns in finite differences: condition number of the matrix. SIAM J. Matrix Anal. Appl. (SIMAX) 14 2 (1993) 432-455
37. Chen M., and Temam R. Nonlinear Galerkin method in finite difference case and wavelet-like incremental unknowns. Numerische Math. 64 (1993) 271-294
38. Chorin A.J. Numerical study of thermal-convection. J. Comput. Phys. 2 (1967) 12-26
39. Chorin A.J. The numerical solution of the Navier-Stokes equations for an incompressible fluid. Bull. Amer. Math. Soc. 73 (1967) 928-931
40. Chorin A.J. Math. Comp. 22 (1968) 745-762
41. Chorin A.J. Stud. Numer. Anal. 2 (1968) 64-71
42. Chorin A.J. Math. Comp. 23 (1969) 341-353
43. Chorin A.J. Vorticity and Turbulence. Applied Math. Sciences 103 (1994), Springer, Berlin
44. Universitext Series. Chorin A.J., and Marsden J.E. A Mathematical Introduction to Fluid Mechanics (1979), Springer, New York
45. Ciarlet P.G. The Finite Element Method for Elliptic Problems (1978), North-Holland, Berlin
46. Part 1. Ciarlet P.G. Basic error estimates for elliptic problems. In: Ciarlet P.G., and Lions J.L. (Eds). Handbook of Numerical Analysis II (1991), North-Holland, Amsterdam 17-352
47. Constantin P., and Foias C. Navier-Stokes Equations (1988), Chicago University Press, Amsterdam
48. Constantin P., Foias C., Manley O., and Temam R. Determining modes and fractal dimension of turbulent flows. J. Fluid Mech. 150 (1985) 427-440
49. 67 + vii pages. Constantin P., Foias C., and Temam R. Attractors representing turbulent flows. Mem. Amer. Math. Soc. 53 114 (1985)
50. Crouzeix M. Approximation et méthodes itératives de résolution d'inéquations variationnelles et de problèmes non linéaires. Cahier de l'IRIA no. 12 (1974) 139-244
51. Daley R. Normal mode initialization. Rev. Geophys. Space Physics 19 (1981) 450-468
52. Daley R. The normal mode approach to the initialization problem. In: Bengtsson L., Ghil M., and Kallen E. (Eds). Dynamic Meteorology, Data Assimilation Methods. Appl. Math. Sci. 36 (1981), Springer, Chicago
53. Dautray L., and Lions J.L. Analyse Mathématique et Calcul Numérique pour les Sciences et les Techniques (1987), Masson, New York
54. Debussche A., Dubois T., and Temam R. The nonlinear Galerkin method: a multiscale method applied to the simulation of homogeneous turbulent flows. Theoret. Comput. Fluid Dynamics 7 (1995) 279-315
55. Debussche A., and Temam R. Inertial manifolds and the slow manifolds in meteorology. Differential Integral Equations 4 5 (1991) 897-931
56. Debussche A., and Temam R. Convergent families of approximate inertial manifolds. J. Math. Pures Appl. 73 (1994) 485-522
57. Dettori L., Gottlieb D., and Temam R. Nonlinear Galerkin method: the two-level Fourier collocation case. J. Sci. Comput. 10 4 (1995) 371-389
58. Dettori L., Gottlieb D., and Temam R. Nonlinear Galerkin method: the two-level Chebyshev-collocation case. Proc. of ICOSAHOM '95. Houston J. Math. (1995) 75-82
59. Devulder C., and Marion M. A class of algorithms for large time integration of evolution equations: the nonlinear Galerkin methods. SIAM J. Numer. Anal. 29 (1992) 462-483
60. Devulder C., Marion M., and Titi E. On the rate of convergence of nonlinear Galerkin methods. Math. Comp. 60 (1993) 495-514
61. Doering C., and Gibbon J.D. Applied Analysis of the Navier-Stokes Equations (1995), Cambridge University Press, Paris
62. to appear. Dubois T., and Jauberteau F. A dynamic model for small structures in homogeneous isotropic turbulence (1996)
63. Dubois T., Jauberteau F., Marion M., and Temam R. Subgrid modelling and the interaction of small and large wavelengths in turbulent flows. Comput. Phys. Commun. 65 (1991) 100-106
64. Dubois T., Jauberteau F., and Temam R. Solution of the incompressible Navier-Stokes equations by the nonlinear Galerkin method. J. Sci. Comput. 8 2 (1993) 167-194
65. Dubois T., Jauberteau F., and Temam R. Dynamical multilevel methods in turbulence simulation. In: Hafez M., and Oshima K. (Eds). Comput. Fluid Dynamic Rev. (1995), J. Wiley, Cambridge 677-694
66. to appear. Dubois T., Jauberteau F., and Temam R. Incremental unknowns, multilevel methods and the numerical simulation of turbulence. Comput. Methods Appl. Mech. (1997)
67. Ekeland I., and Temam R. Analyse Convexe et Problèmes Variationnels. Collection Etudes Mathématiques (1974), Dunod, New York
68. Convex Analysis and Variational Problems (1976), North-Holland, Paris
69. Fletcher C.A.J. Computational Galerkin Methods. Series in Computational Physics (1984), Springer, Amsterdam
70. Foias C., Jolly M.S., Kevrekidis I.G., Sell G.R., and Titi E.S. On the computation of inertial manifolds. Phys. Lett. A 131 (1988) 433-436
71. Foias C., Jolly M.S., Kevrekidis I.G., and Titi E.S. Dissipativity of numerical schemes. Nonlinearity 4 (1991) 591-631
72. Série I. Foias C., Manley O., and Temam R. Sur l'interaction des petits et grands tourbillons dans les écoulements turbulents. C. R. Acad. Sci. Paris 305 (1987) 497-500
73. Foias C., Manley O., and Temam R. Modelization of the interaction of small and large eddies in two dimensional turbulent flows. Math. Model. and Numer. Anal. (M2AN) 22 (1988) 93-114
74. Foias C., Manley O., Temam R., and Trève Y. Number of modes governing two-dimensional viscous incompressible flows. Phys. Rev. Lett. 50 (1983) 1031-1034
75. Série I. Foias C., Sell G., and Temam R. Variétés inertielles des équations différentielles dissipatives. C. R. Acad. Sci. Paris 300 (1985) 139-142
76. Foias C., Sell G., and Temam R. Inertial manifolds for nonlinear evolutionary equations. J. Differential Equations 73 (1988) 309-353
77. Foias C., and Temam R. Some analytic and geometric properties of the evolution Navier-Stokes equations. J. Math. Pures Appl. 58 (1979) 339-368
78. Foias C., and Temam R. Gevrey class regularity for the solutions of the Navier-Stokes equations. J. Funct. Anal. 87 (1989) 359-369
79. (in Russian). Fursikov A.V. On some problems of control. Dokl. Akad. Nauk SSSR (1980) 1066-1070
80. Girault V., and Raviart P.A. Finite Elements Methods for Navier-Stokes Equations. Series in Computational Mathematics 5 (1986), Springer, New York
81. Glowinski R. Numerical Methods for Nonlinear Variational Problems (1984), Springer, New York
82. Gottlieb D., and Orszag S.A. Numerical Analysis of Spectral Methods, Theory and Applications (1977), SIAM Publications, New York
83. Gottlieb D., and Temam R. Implementation of the nonlinear Galerkin method with pseudo-spectral (collocation) discretization. Appl. Numer. Math. 12 (1993) 119-134
84. Série I. Goubet O. Séparation des variables dans le problème de Stokes. Application à son approximation multiéchelles éléments finis. C. R. Acad. Sci. Paris 315 (1992) 1315-1318
85. to appear. Goubet O. Separation of variables in the Stokes problem. Application to its finite element multiscale approximation (1993)
86. Gresho P.M. On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly consistent mass matrix. Part 1, Theory. Internat. J. Numer. Methods Fluids 11 (1990) 587-620
87. Gresho P.M. Incompressible fluid dynamics: some fundamental formulation issues. Annual Rev. Fluid Mech. 23 (1991) 413-453
88. Gresho P.M. Some current CFD issues relevant to the incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg. 87 (1991) 201-252
89. Gresho P.M. Some interesting issues in incompressible fluid dynamics, both in continuum and in numerical simulation. Advances in Applied Mechanics 28 (1992) 45-140
90. Gresho P.M., and Chan S. On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly consistent mass matrix. Part 2. Implementation. Internat. J. Numer. Methods Fluids 11 (1990) 621-659
91. book in preparation. Gresho P.M., and Sani R.L. Incompressible Flow and the Finite Element Method, I: Advection Diffusion and Isothermal Laminar Flow (1996)
92. Gunzburger M.D. Finite Element Methods for Viscous Incompressible Flows (1989), Academic Press, Philadelphia
93. Hale J. Asymptotic Behaviour of Dissipative Systems. Mathematical Surveys and Monographs 25 (1988), AMS, Boston
94. Halpern L., and Schatzman M. Artificial boundary conditions for incompressible viscous flow. SIAM J. Math. Anal. 70 2 (1989) 308
95. Haugel A., and Cahouet J. Finite element methods for incompressible Navier-Stokes equations and for shallow water equations (1986), EDF, Laboratoire National d'Hydraulique, Providence, RI
96. Preprint. He Y., and Li K. Nonlinear Galerkin method and two-step method for the Navier-Stokes equations (1995), Xi'an Jiaotong University, Chatou, France
97. Henshaw W.D., Kreiss H.O., and Reyna L.G. On the smallest scale for the incompressible Navier-Stokes equations. Theoret. Comput. Fluid Dynamics 1 (1989) 65-95
98. Henshaw W.D., Kreiss H.O., and Reyna L.G. Smallest scale estimates for the incompressible Navier-Stokes equations. Arch. Rational Mech. Anal. 112 (1990) 21-44
99. The Navier-Stokes Equations. Theory and Numerical Methods. In: Heywood J.G., Masuda K., Rautmann R., and Solonnikov V.A. (Eds). Proc. of the Conference held in Oberwolfach. September 18-24, 1988. Lecture Notes in Math. 1431 (1990), Springer
100. Heywood J.G. Classical solutions of the Navier-Stokes equations. In: Rautman R. (Ed). Proc. IUTAM Symp. Paderbon, 1979. Lecture Notes in Math. 771 (1980), Springer, New York
101. The Navier-Stokes Equations II. Theory and Numerical Methods. In: Heywood J.G., Masuda K., Rautmann R., and Solonnikov V.A. (Eds). Proc. of the Second Conference held in Oberwolfach. August 18-24, 1991. Lecture Notes in Math. 1530 (1991), Springer, New York
102. Heywood J.G., and Rannacher R. Finite element approximation of the nonstationary Navier-Stokes problem. I. Regularity of solutions and second-order error estimates for spatial discretization. SIAM J. Numer. Anal. 19 (1982) 275-311
103. Heywood J.G., and Rannacher R. On the question of turbulence modeling by approximate inertial manifolds and the nonlinear Galerkin method. SIAM J. Numer. Anal. 30 no. 6 (1993) 1603-1621
104. Chichester, England. Hirsch Ch. Numerical Computational of Internal and External Flows (1988), J. Wiley, New York
105. Jauberteau F., Rosier C., and Temam R. The nonlinear Galerkin method in computational fluid dynamics. Appl. Numer. Math. 6 (1989) 361-370
106. Jauberteau F., Rosier C., and Temam R. A nonlinear Galerkin method for the Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg. 80 (1990) 245-260
107. Jolly M. Bifurcation computations on an approximate inertial manifold for the Navier-Stokes equations. Physica 63D (1993) 8-20
108. Jolly M.S., and Xiong C. On computing the long-time solution of the two-dimensional Navier-Stokes equation. Theoret. Comput. Fluid Dynamics 7 4 (1995) 261-278
109. Jones D.A., Margolin L.G., and Titi E.S. On the effectiveness of the approximate inertial manifold-A computational study. Theoret. Comput. Fluid Dynamics 7 4 (1995) 243-260
110. Karniadakis G.E., Israeli M., and Orszag S.A. High-order splitting methods for the incompressible Navier-Stokes equations. J. Comput. Phys. 97 (1991) 414-443
111. Kim, J. (1989), Personal communication.
112. Kim J., and Moin P. Application of a fractional-step method to incompressible Navier-Stokes equations. J. Comput. Phys. 59 (1985) 308-323
113. Kolmogorov A.N. The local structure of turbulence in incompressible viscous fluid for very large Reynolds number. C. R. Acad. Sci. URSS 30 (1941) 301
114. Kolmogorov A.N. On degeneration of isotropic turbulence in an incompressible viscous liquid. C.R. Acad. Sci. URSS 31 (1941) 538
115. Kolmogorov A.N. Dissipation of energy in locally isotropic turbulence. C. R. Acad. Sci. URSS 32 (1941) 16
116. Kraichnan R.H. Inertial ranges in two-dimensional turbulence. Phys. Fluids 10 (1967) 1417-1423
117. Ladyzhenskaya O.A. Mathematical Problems in the Dynamics of Viscous Incompressible Flow (1963), Gordon and Breach, New York
118. Ladyzhenskaya O.A. Attractors for Semigroups and Evolution Equations (1991), Cambridge University Press, New York
119. Lamb H. Hydrodynamics (1932), Dover, Cambridge
120. Laminie J., and Meier U. Solving Navier-Stokes equations on the Cedar multi-cluster system. Technical Note (1990), Center for Supercomputing Research and Development (CSRD), University of Illinois, New York
121. Laminie J., Pascal F., and Temam R. Implementation of finite element nonlinear Galerkin methods using hierarchical bases. J. Comput. Mech. 11 (1993) 384-407
122. Laminie J., Pascal F., and Temam R. Implementation and numerical analysis of the nonlinear Galerkin methods with finite elements discretizations. Appl. Numer. Math. 15 (1994) 219-246
123. Landau L., and Lifschitz E. Fluid Mechanics (1953), Addison-Wesley, Urbana-Champaign
124. Lemonnier P. Résolution numérique d'équations aux dérivées partielles par décomposition et coordination. Cahier de l'IRIA no. 11 (1972)
125. Leray J. Etude de diverses équations intégrales non linéaires et de quelques problèmes que pose l'hydrodynamique. J. Math. Pures Appl. 12 (1933) 1-82
126. Leray J. Essai sur les mouvements plans d'un liquide visqueux que limitent des parois. J. Math. Pures Appl. 13 (1934) 331-418
127. Leray J. Essai sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Math. 63 (1934) 193-248
128. In: Lichnewsky A., and Saguez C. (Eds). Supercomputing (1987), North-Holland, New York
129. Preprint, 27 pages. Li K., and Yanren H. Fourier nonlinear Galerkin method for Navier-Stokes equations (1995)
130. Li K., Huang A., and He Y. Full discrete nonlinear Galerkin method. In: Lungan Y., and Benyu G. (Eds). Proc. of the Second Conference on Numerical Methods for PDE (1992), World Scientific, Amsterdam 61-82
131. Ser. 1. Li K., Huang A., and He Y. Full discrete nonlinear Galerkin method for the Navier-Stokes equations. Appl. Math. J. Chinese Univ. 9 1 (1994) 11-30
132. Lions J.L. Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires (1969), Dunod
133. Lions J.L., and Magenes E. Problèmes aux Limites non Homogènes et Applications I (1968), Dunod, Paris
134. Lions J.L., and Magenes E. Nonhomogeneous Boundary Value Problems and Applications (1972), Springer, Paris
135. Special issue in honor of Jameson. Lions J.L., Temam R., and Wang S. Splitting-up methods and numerical analysis of some multiscale problems. Comput. Fluid Dynamics 5 2 (1996) 157-202
136. Lions P.L. Mathematical Topics in Fluid Mechanics I, Incompressible Models. Series in Mathematics and its Applications 3 (1996), Oxford University Press, New York
137. Preprint. Liou J., and Tezduyar T.E. Numerical simulation of a periodic array of cylinders between two parallel walls. Ercoftac Workshop: problem T2 (1990)
138. Liu V.X. A sharp lower bound for the Hausdorff dimension of the global attractor of the 2D Navier-Stokes equations. Comm. Math. Phys. 158 (1993) 327-339
139. Lorenz E.N. Determinic nonperiodic flow. J. Atmospheric Sci. 20 (1963) 130-141
140. Lorenz E.N. The Nature and Theory of the General Circulation of the Atmosphere (1967), World Meteorological Organization, New York
141. Lorenz E.N. Attractors sets and quasi-geostrophic equilibrium. J. Atmospheric Sci. 37 (1980) 1685-1699
142. Machenhauer B.A. On the dynamics of gravity oscillations in a shallow water model with applications to normal mode initialization. Beitr. Phys. Atmos. 10 (1977) 253-271
143. Magenes E., and Stampacchia G. I problemi al contorno per le equzioni differenziali di tipo ellitico. Ann. Scuola Norm. Sup. Pisa 12 (1958) 247-357
144. Majda A. Compressible fluid flow and systems of conservation laws in several space variables. Applied Math. Sciences Series 53 (1984), Springer
145. Majda A. The interaction of nonlinear analysis and modern applied mathematics. Proc. International Congress of Mathematicians. Kyoto (1990)
146. Marchuk G.I. Splitting and alternating direction methods. In: Ciarlet P.G., and Lions J.L. (Eds). Handbook of Numerical Analysis I (1990), North-Holland, Berlin 197-462
147. Marion M. Approximate inertial manifolds for reaction-diffusion equations in high space dimension. Dynamics and Differential Equations 1 (1989) 245-267
148. Marion M. Approximate inertial manifolds for the pattern formation Cahn-Hilliard equation. Math. Model. and Numer. Anal. (M2AN) 23 (1989) 463-488
149. Marion M., and Debussche A. On the construction of families of approximate inertial manifolds. J. Differential Equations 100 (1992) 173-201
150. Marion M., and Temam R. Nonlinear Galerkin methods. SIAM J. Numer. Anal. 29 (1989) 1139-1157
151. Marion M., and Temam R. Nonlinear Galerkin methods. The finite elements case. Numer. Math. 57 (1990) 205-226
152. Marion M., and Xu J. Error estimates for a new nonlinear Galerkin method based on two-grid finite elements. SIAM J. Numer. Anal. 32 (1995) 1170-1184
153. Orszag S.A. Lectures on the statistical theory of turbulence. Proc. of the Summer School in Theoretical Physics. Les Houches (1973)
154. Orszag S.A., Israeli M., and Deville M.O. Boundary conditions for incompressible flows. J. Sci. Comput. 1 (1986) 75-111
155. Preprint. Pasero D. Time discretization of nonlinear evolution equations based on multiple scale spatial splitting (1996)
156. Peyret R., and Taylor T.D. Computational Methods for Fluid Flow (1983), Springer, Amsterdam
157. Série I. Pironneau O. Partial differential equations (Numerical analysis)-boundary conditions on the pressure for the Stokes and the Navier-Stokes equations. C. R. Acad. Sci. Paris 303 (1986)
158. Série I. Pironneau O. Mathematical problems in mechanics going back to Stokes and Navier-Stokes equations with boundary conditions on the pressure. C. R. Acad. Sci. Paris 303 (1987) 23
159. Pironneau O. Méthode des Éléments Finis pour les Fluides. Collection Recherches en Mathématiques Appliquées 7 (1988), Masson, New York
160. Part 1. Roberts J., and Thomas J.M. Mixed and hybrid methods. In: Ciarlet P.G., and Lions J.L. (Eds). Handbook of Numerical Analysis II (1991), North-Holland, Paris 523-639
161. Sani R.L., Eaton B.E., Gresho P.M., Lee R.L., and Chan S.T. On the solution of the time-dependent incompressible Navier-Stokes equations via a penalty Galerkin finite element method. In: Taylor C., and Schreffler B.S. (Eds). Proc. of the International Conference on Numerical Methods for Laminar and Turbulent Flows (1981) 41-51
162. Sani R.L., and Gresho P.M. Resume and remarks on the open boundary condition minisymposium. Internat J. Numer. Methods Fluids 18 (1994)
163. Shen J. Convergence of the approximate attractors for a fully discrete scheme for the reaction-diffusion equation. Numer. Funct. Anal. Optim. 10 11-12 (1989) 1213-1234
164. Shen J. Hopf bifurcation of the unsteady regularized driven cavity flows. J. Comput. Phys. 95 (1991) 228-245
165. Shen J. On error estimates of projection methods for Navier-Stokes equations: first-order schemes. SIAM J. Numer. Anal. 29 1 (1992) 57-77
166. Shen J. On error estimates of some higher order projection and penalty projection methods for Navier-Stokes equations. Numer. Math. 62 (1992) 49-73
167. Shen J. Remarks on the pressure error estimates for the projection methods. Numer. Math. 17 (1994) 513-520
168. Shen J. On error estimates of penalty method for unsteady Navier-Stokes equations. SIAM J. Numer. Anal. 32 (1995) 386-403
169. Shen J., and Temam R. Nonlinear Galerkin method using Chebyshev and Legendre polynomials I. The one dimensional case. SIAM J. Numer. Anal. 32 (1995) 215-234
170. Tachim-Medjo T. Vorticity-velocity formulation for the stationary Navier-Stokes equations: the three dimensional case. Appl. Math. Lett. 8 (1995) 63-66
171. Tachim-Medjo T. Navier-Stokes equations in the vorticity-velocity formulation: the two-dimensional case. Appl. Numer. Math. 21 (1996) 185-206
172. Tachim-Medjo T. Vorticity-velocity formulation for the stationary Navier-Stokes equations: the three-dimensional case. Numerical Methods Partial Differential Equations 12 (1996) 1-20
173. Série A. Temam R. Sur l'approximation des équations de Navier-Stokes. C. R. Acad. Sci. Paris 262 (1966) 219-221
174. Série A. Temam R. Sur l'approximation de la solution d'équations d'évolution par la méthode des pas fractionnaires. C. R. Acad. Sci. Paris 263 (1966) 241-244
175. Série A. Temam R. Sur l'approximation de la solution d'équations d'évolution par la méthode des pas fractionnaires. C. R. Acad. Sci. Paris 263 (1996) 265-267
176. Série A. Temam R. Sur l'approximation de la solution d'équations d'évolution par la méthode des pas fractionnaires. C. R. Acad. Sci. Paris 263 (1966) 459-462
177. Série 4. Temam R. Sur la stabilité et la convergence de la méthode des pas fractionnaires. Ann. Mat. Pura Appl. LXXIV (1968) 191-380
178. Temam R. Une méthode d'approximation de la solution des équations de Navier-Stokes. Bull. Soc. Math. France 98 (1968) 115-152
179. Temam R. Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires (I). Arch. Rational Mech. Anal. 33 (1969) 377-385
180. Temam R. Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires (II). Arch. Rational Mech. Anal. 33 (1969) 377-385
181. Temam R. On the Euler equations of incompressible perfect fluids. J. Funct. Anal. 20 (1975) 32-43
182. Temam R. Behaviour at time t = 0 of the solutions of semi-linear evolution equations. J. Differential Equations 17 (1982) 73-92
183. Temam R. Navier-Stokes Equations and Nonlinear Functional Analysis. CMBS-NSF Regional Conference Series in Applied Mathematics (1983), SIAM, Amsterdam
184. Temam R. Navier-Stokes Equations. 3rd revised edition (1984), North-Holland, Philadelphia
185. (AMS). Temam R. Remarks on Euler equations. In: Browder F. (Ed). Nonlinear Functional Analysis and its Applications. Proceedings of Symposia in Pure Mathematics 45 (1986) 429-430
186. Temam R. Induced trajectories and approximate inertial manifolds. Math. Model. and Num. Anal. (M2AN) 23 (1989) 541-561
187. Sec. IA. Temam R. Attractors for the Navier-Stokes equations, Localization and Approximation. J. Fac. Sci. Tokyo 36 (1989) 629-647
188. Temam R. Inertial Manifolds. Math. Intelligencer 12 4 (1990) 68-74
189. Temam R. Remark on the pressure boundary condition for the projection method. Theoret. Comput. Fluid Dynamics 3 (1991) 181-184
190. In: Temam R. (Ed). Inertial Manifolds and their Application to the Simulation of Turbulence. Special Issue of Theoret. Comput. Fluid Dynamics 7 (1995) 4
191. Temam R. Infinite Dimensional Dynamical Systems in Mechanics and Physics. Applied Mathematical Sciences Series. 2nd augmented edition 68 (1997), Springer, Amsterdam
192. Thomasset F. Implementation of Finite Elements Methods for Navier-Stokes Equations. Series in Computational Physics (1981), Springer, New York
193. Titi E.S. On approximate inertial manifolds to the Navier-Stokes equations. J. Math. Anal. Appl. 149 (1990) 540-557
194. Tribbia J.J. Nonlinear initialization on an equatorial Bet-plane. Mon. Wea. Rev. 107 (1979) 704-713
195. Tribbia J.J. On variational normal mode initialization. Mon. Wea. Rev. 110 (1982) 455-470
196. Tribbia J.J. A simple scheme for high-order normal mode initialization. Mon. Wea. Rev. 112 (1984) 278-284
197. Van Kan J. A second-order accurate pressure-correction scheme for viscous incompressible flow. SIAM J. Sci. Statist. Comput. 7 (1986) 870-891
198. Von Wahl W. The Equations of Navier-Stokes and Abstract Parabolic Equations. Aspects of Mathematics E8 (1985), Friedr. Vieweg & Sohn, New York
199. (in Russian). Yanenko N.N. The Method of Fractional Steps for Multidimensional Problems in Mathematical Physics. English translation (1966) English translation
200. (in Russian). Yanenko N.N. The Method of Fractional Steps for Multidimensional Problems in Mathematical Physics. English translation. Théorie des Pas Fractionnaires (1968), Armand Colin, Braunschweig English translation
201. (in Russian). Yanenko N.N. The Method of Fractional Steps for Multidimensional Problems in Mathematical Physics. English translation. The Method of Fractional Steps (1971), Springer, Paris
202. Yserentant H. On the multi-level splitting of finite elements. Numer. Math. 49 (1986) 379-412
203. Yserentant H. Two preconditioners based on the multi-level splitting of finite elements. Numer. Math. 58 (1990) 163-184