Two-Level Stabilized Finite Volume Methods for the Stationary Navier-Stokes Equations (Advances in Applied Mathematics and Mechanics, 2018)
In this work, two-level stabilized finite volume formulations for the2D steady Navier-Stokes equations are considered.These methods are basedon the local Gauss integration technique and the lowest equal-orderfinite element pair. Moreover, the two-levelstabilized finite volume methods involve solving one small Navier-Stokesproblem on a coarse mesh with mesh size $H$, a large general Stokes problem for the Simple andOseen two-level stabilized finite volume methods on the fine mesh with mesh size $h$=$\mathcal{O}(H^2)$ or a large general Stokes equations for the Newton two-level stabilized finitevolume method on a fine mesh with mesh size $h$=$\mathcal{O}(|\log h|^{1/2}H^3)$.These methods we studied provide anapproximate solution $(\widetilde{u}_h^v,\widetilde{p}_h^v)$ with the convergence rate of same orderas the standard stabilized finite volume method, which involve solving one largenonlinear problem on a fine mesh with mesh size $h$. Hence, our methodscan save a large amount of computational time.