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A two-grid method based on Newton iteration for the Navier–Stokes equations

✍ Scribed by Xiaoxia Dai; Xiaoliang Cheng

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
158 KB
Volume
220
Category
Article
ISSN
0377-0427

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✦ Synopsis

In this paper, we consider a two-grid method for resolving the nonlinearity in finite element approximations of the equilibrium Navier-Stokes equations. We prove the convergence rate of the approximation obtained by this method. The two-grid method involves solving one small, nonlinear coarse mesh system and two linear problems on the fine mesh which have the same stiffness matrix with only different right-hand side. The algorithm we study produces an approximate solution with the optimal asymptotic in h and accuracy for any Reynolds number. Numerical example is given to show the convergence of the method.

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