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

Fairag, Faisal (1998) A two-level finite-element discretization of the stream function form of the Navier-Stokes equations. Comput. Math. Appl., 36 (2). pp. 117-127.

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## Abstract

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 $|\psi- \psi^h|_2\le C\left\{ \inf_{w^h\in X^h}|\psi- w^h|_2+ |\ln h|^{1/2}\cdot|\psi- \psi^H|_1\right\}$. 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 $h= O(H^{3/2}|\ln H|^{1/4})$.

Item Type: Article Naviex-Stokes equations, Reynolds number, Finite element, Two-level methods, Stream function formulation. 1998 Publication Math College Of Sciences > Mathematical Science Dept Fairag, Faisal ffairag@kfupm.edu.sa 1250 FAISAL ABDULKARIM M FAIRAG 05 May 2008 12:07 12 Apr 2011 13:08

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