NDLI: Development of the collocations and least squares method

Content Provider	Springer Nature Link
Author	Isaev, V. I. Shapeev, V. P.
Copyright Year	2008
Abstract	We propose and implement new, more general versions of the method of collocations and least squares (the CLS method) and, for a system of linear algebraic equations, an orthogonal method for accelerating the convergence of an iterative solution. The use of the latter method and the proper choice of values of control parameters, based on the results of investigating the dependence of the properties of the CLS method on these parameters, as well as some other improvements of the CLS method suggested in this paper, allow one to solve numerically problems for Navier-Stokes equations in a reasonable time using a single-processor computer even for grids as large as 1280 × 1280. In this case, the total number of unknown variables is ∼ 25 · 10$^{6}$. The numerical results for the problem of the lid-driven cavity flow of a viscous fluid are in good agreement with known results of other authors, including those obtained by means of schemes of higher approximation order with a small artificial viscosity. This and some other facts prove that the new versions of the CLS method make it possible to obtain an approximate solution with high accuracy.
Starting Page	87
Ending Page	106
Page Count	20
File Format	PDF
ISSN	00815438
Journal	Proceedings of the Steklov Institute of Mathematics
Volume Number	261
Issue Number	1
e-ISSN	15318605
Language	English
Publisher	SP MAIK Nauka/Interperiodica
Publisher Date	2009-05-24
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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