Li, Kaitai; He, Yinnian; Xiang, Yimin Full discrete nonlinear Galerkin method for the Navier-Stokes equations. (English) Zbl 0807.76038 Appl. Math., Ser. B (Engl. Ed.) 9, No. 1, 11-30 (1994). This paper deals with the inertial manifold and the approximate inertial manifold concepts for the Navier-Stokes equations with nonhomogeneous boundary conditions. Furthermore, we provide error estimates for the approximate solutions. Cited in 2 Documents MSC: 76M10 Finite element methods applied to problems in fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs Keywords:fractional step method; inertial manifold; approximate inertial manifold; error estimates PDFBibTeX XMLCite \textit{K. Li} et al., Appl. Math., Ser. B (Engl. Ed.) 9, No. 1, 11--30 (1994; Zbl 0807.76038) Full Text: DOI References: [1] Foias, C., Sell, G. & Temam, R., Inertial manifolds for nonlinear evolutionary equations,J. Differential Equation,73 (1988), 309–353. · Zbl 0643.58004 · doi:10.1016/0022-0396(88)90110-6 [2] Foias, C., Nicolaerenko, B., Sell, G. & Temam, R., Inertial manifolds for the Kuramoto-Sivashinsky equation and on estimate of their lowest dimension,J. Maht. Pure. Appl.,67 (1988), 197–226. · Zbl 0694.35028 [3] Glowinski, R., Muntel, B., Periaux, J. & Pironneau, D., A finite element approximation of Navier-Stokes equations for incompressible viscous fluids, functional least squares method of solution, In: Morgan, K., Toylor, K., Brebbia, A., Computer Methods in Fluids (84–113), London Pentech Press, 1980. [4] Constantin, P., Foias, C., Nicoloenko B. & Temam, R., Attractor for the Benard problem: Existence & physical bounds on their fractal dimension,Nonlinear Anal: Theory method Appl.,11 (1987), 939–967. · Zbl 0646.76098 · doi:10.1016/0362-546X(87)90061-7 [5] Foias, C., Manley, O. & Temam, R., Modelization of the international of small & large eddies in turbulent flows,RAIRO Math. Model. Anal. Numer,22 (1988), 93–114. · Zbl 0663.76054 [6] Enrique Fernandez-Cara & Mercedes Marin Beltran, The convergence of two numerical schemes for the Navier-Stokes equations,Numer. Math.,55 (1989), 33–60. · Zbl 0645.76032 · doi:10.1007/BF01395871 [7] Temam, R., Navier-Stokes Equations, Third Edition, North-Holland, Amsterdam, New York, 1984. · Zbl 0568.35002 [8] Mariou, M. and Temam, R., Nonlinear Galerkin methods,SIAM J. Numer. Anal.,26: 5 (1989), 1139–1157. · Zbl 0683.65083 · doi:10.1137/0726063 [9] Girault, Y., Raviart, P. A., Finite Element Approximation of the Navier-Stokes Equations, Lectures Note in Math.,749, Springer-Verlag, 1979. · Zbl 0413.65081 [10] Marion, M. & Temam, R., Nonlinear Galerkin methods: The finite element case.Numer. Math.,57 (1990), 205–226. · Zbl 0702.65081 · doi:10.1007/BF01386407 [11] Brezz, F., Douglas, J. & Morini, L. D., Two families of mixed finite element for second order elliptic problems,Numer. Math.,47 (1985), 217–235. · Zbl 0599.65072 · doi:10.1007/BF01389710 [12] Titi, E. S., On approximate inertial manifolds to the Navier-Stokes equations,J. Math. Anal. Appl.,149 (1990), 540–557. · Zbl 0723.35063 · doi:10.1016/0022-247X(90)90061-J [13] Derulder, C. and Marion, M., A class of numerical algorithms for large time integration: the nonlinear Galerkin methods,SIAM J. Numer. Anal.,29 (1992), 462–483. · Zbl 0754.65080 · doi:10.1137/0729028 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.