NDLI: Two-level Stabilized Finite Element Methods for the Steady Navier

Content Provider	Springer Nature Link
Author	He, Yinnian Li, Kaitai
Copyright Year	2005
Abstract	In this article, the two-level stabilized finite element formulations of the two-dimensional steady Navier–Stokes problem are analyzed. A macroelement condition is introduced for constructing the local stabilized formulation of the steady Navier–Stokes problem. By satisfying this condition the stability of the Q1−P0 quadrilateral element and the P1−P0 triangular element are established. Moreover, the two-level stabilized finite element methods involve solving one small Navier–Stokes problem on a coarse mesh with mesh size H, a large Stokes problem for the simple two-level stabilized finite element method on a fine mesh with mesh size h=O(H2) or a large general Stokes problem for the Newton two-level stabilized finite element method on a fine mesh with mesh size h=O(\|log h\|1/2H3). The methods we study provide an approximate solution (uh,ph) with the convergence rate of same order as the usual stabilized finite element solution, which involves solving one large Navier–Stokes problem on a fine mesh with mesh size h. Hence, our methods can save a large amount of computational time.
Starting Page	337
Ending Page	351
Page Count	15
File Format	PDF
ISSN	0010485X
Journal	Computing
Volume Number	74
Issue Number	4
e-ISSN	14365057
Language	English
Publisher	Springer-Verlag
Publisher Date	2005-02-16
Publisher Place	Vienna
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Navier–Stokes problem stabilized finite element two-level method error estimate Computational Mathematics and Numerical Analysis
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Computational Theory and Mathematics Computational Mathematics Numerical Analysis Computer Science Applications Software

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