A two-level finite-element discretization of the stream function form of the Navier-Stokes equations

We analyze a two-level method of discretizing the stream function form of the Navier-Stokes equations. This report presents the two-level algorithm and error analysis for the case of conforming elements. The two-level algorithm consists of solving a small nonlinear system on the coarse mesh, then solving a linear system on the fine mesh. The basic result states that the error between the coarse and fine meshes are related superlinearly via: |ψ-ψ^h|₂≤C{inf_wh∈Xh|ψ-w ^h|₂+|ln h|^1/2·|ψ-ψ^H|₁}· As an example, if the Clough-Tocher triangles or the Bogner-Fox-Schmit rectangles are used, then the coarse and fine meshes are related by h = O(H^3/2|ln H|^1/4).