TWO-LEVEL MULTISCALE FINITE ELEMENT METHODS FOR THE STEADY NAVIER-STOKES PROBLEM

doi:10.1016/S0252-9602(14)60062-X

Abstract

Abstract:

In this article, on the basis of two-level discretizations and multiscale finite el-ement method, two kinds of finite element algorithms for steady Navier-Stokes problem are presented and discussed. The main technique is first to use a standard finite element dis-cretization on a coarse mesh to approximate low frequencies, then to apply the simple and Newton scheme to linearize discretizations on a fine grid. At this process, multiscale finite element method as a stabilized method deals with the lowest equal-order finite element pairs not satisfying the inf-sup condition. Under the uniqueness condition, error analyses for both algorithms are given. Numerical results are reported to demonstrate the effectiveness of the simple and Newton scheme.

Key words: Multiscale finite element method, two-level method, error analysis, the Navier-Stokes problem

WEN Juan, HE Yin-Nian, WANG Xue-Min, HE Mi-Hui. TWO-LEVEL MULTISCALE FINITE ELEMENT METHODS FOR THE STEADY NAVIER-STOKES PROBLEM[J].Acta mathematica scientia,Series B, 2014, 34(3): 960-972.

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