Two-Level Stabilized Finite Volume Methods for Stationary Navier-Stokes Equations

Abstract

We propose two algorithms of two-level methods for resolving the nonlinearity in the stabilized finite volume approximation of the Navier-Stokes equations describing the equilibrium flow of a viscous, incompressible fluid. A macroelement condition is introduced for constructing the local stabilized finite volume element formulation. Moreover the two-level methods consist of solving a small nonlinear system on the coarse mesh and then solving a linear system on the fine mesh. The error analysis shows that the two-level stabilized finite volume element method provides an approximate solution with the convergence rate of the same order as the usual stabilized finite volume element solution solving the Navier-Stokes equations on a fine mesh for a related choice of mesh widths.