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Two-Level Stabilized Finite Volume Methods for the Stationary Navier-Stokes Equations
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- Journal:
- Advances in Applied Mathematics and Mechanics / Volume 5 / Issue 1 / February 2013
- Published online by Cambridge University Press:
- 03 June 2015, pp. 19-35
- Print publication:
- February 2013
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- Article
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In this work, two-level stabilized finite volume formulations for the 2D steady Navier-Stokes equations are considered. These methods are based on the local Gauss integration technique and the lowest equal-order finite element pair. Moreover, the two-level stabilized finite volume methods involve solving one small Navier-Stokes problem on a coarse mesh with mesh size H, a large general Stokes problem for the Simple and Oseen two-level stabilized finite volume methods on the fine mesh with mesh size
or a large general Stokes equations for the Newton two-level stabilized finite volume method on a fine mesh with mesh size 
. These methods we studied provide an approximate solution 
with the convergence rate of same order as the standard stabilized finite volume method, which involve solving one large nonlinear problem on a fine mesh with mesh size h. Hence, our methods can save a large amount of computational time.
or a large general Stokes equations for the Newton two-level stabilized finite volume method on a fine mesh with mesh size 
. These methods we studied provide an approximate solution 
with the convergence rate of same order as the standard stabilized finite volume method, which involve solving one large nonlinear problem on a fine mesh with mesh size 