FULL DISCRETE TWO-LEVEL CORRECTION SCHEME FOR NAVIER-STOKES EQUATIONS 被引量：1

FULL DISCRETE TWO-LEVEL CORRECTION SCHEME FOR NAVIER-STOKES EQUATIONS

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摘要 In this paper, a full discrete two-level scheme for the unsteady Navier-Stokes equations based on a time dependent projection approach is proposed. In the sense of the new projection and its related space splitting, non-linearity is treated only on the coarse level subspace at each time step by solving exactly the standard Galerkin equation while a linear equation has to be solved on the fine level subspace to get the final approximation at this time step. Thus, it is a two-level based correction scheme for the standard Galerkin approximation. Stability and error estimate for this scheme are investigated in the paper. In this paper, a full discrete two-level scheme for the unsteady Navier-Stokes equations based on a time dependent projection approach is proposed. In the sense of the new projection and its related space splitting, non-linearity is treated only on the coarse level subspace at each time step by solving exactly the standard Galerkin equation while a linear equation has to be solved on the fine level subspace to get the final approximation at this time step. Thus, it is a two-level based correction scheme for the standard Galerkin approximation. Stability and error estimate for this scheme are investigated in the paper.

作者 Yanren Hou Liquan Mei

机构地区 College of Science

出处《Journal of Computational Mathematics》 SCIE EI CSCD 2008年第2期209-226,共18页 计算数学（英文）

基金 subsidized by the State Basic Research Project (Grant No.2005CB32703) NSF of China (Grant No.10471110) and NCET

关键词 Two-level method Galerkin approximation CORRECTION Navier-Stokes equation Two-level method Galerkin approximation Correction Navier-Stokes equation

分类号 O175.1 [理学—基础数学]

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1A.A.O. Ammi and M. Marion, Nonlinear Galerkin methods and mixed finite elements: Two-grid algorithms for the Navier-Stokes equations, Numer. Math., 68 (1994), 189-213.
2H. Brezis and T. Gallouet, Nonlinear Schroedinger evolution equations, Nonlinear Anal., 4 (1980), 667-681.
3C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang, Spectral Methods in Fluid Dynamics, Springer-Verlag, New York-Heidelberg-Berlin, 1987.
4C. Devulder, M. Marion and E.S. Titi, On the rate of convergence of nonlinear Galerkin methods, Math. Comput., 60 (1993), 495-514.
5C. Foias, O. Manley and R. Temam, On the interaction of small eddies in two-dimensional turbulence flows, Math. Model. Numer. Anal., 22 (1988), 93-114.
6B. Garcia-Achilla, J. Novo and E. Titi, Post-processing the Galerkin method: A novel approch to approximate inertial manifolds, SIAM J. Numer. Anal., 35 (1998), 942-972.
7B. Garcia-Achilla, J. Novo and E. Titi, An approximate inertial manifolds approach to post- processing the Qalerkin method for the Navier-Stokes equations, Math. Comput., 68 (1999), 893-911.
8V. Girault and J.L. Lions, Two-grid finite element scheme for the transient Navier-Stokes problem, Math. Model. Numer. Anal., 35 (2001), 945-980.
9V. Girault and P-A. Raviart, Finite Element Methods for the Navier-Stokes Equations, Theory and Algorithms, Springer Verlag, Berlin, 1986.
10J.G. Heywood and R. Rannacher, Finite element approximation of the nonstationary Navier- Stokes problems, Part Ⅰ. Regularity of solutions and second-order error estimates for partial discretization, SIAM J. Numer. Anal., 19 (1982), 275-311.