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Two-level Stabilized Finite Element Methods for the Steady Navier–Stokes Problem
Computing 74, 337-351 (2005),-0001,():
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.
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