A combined conjugate gradient-multigrid algorithm for the numerical solution of the Stokes problem. (English) Zbl 0563.76028

Verfürth, R.

IMA J. Numer. Anal. 4, 441-455 (1984).

The finite-element discretization of the Stokes problem in a bounded domain \(\Omega\) leads to an equation \(Lp=g\) for the pressure, where L is a symmetric, positive definite, bounded linear operator in \(L^ 2(\Omega)\). This equation is solved by a conjugate-gradient algorithm. Evaluating Lp requires the solution of two discrete Poisson equations by a multigrid algorithm. The resulting iterative process has a convergence rate bounded away from one, independently of the meshsize, and computed between 0.8 and 0.93 by numerical experiments.

Reviewer: M.Boudouvides

MSC:

76D05	Navier-Stokes equations for incompressible viscous fluids
76-04	Software, source code, etc. for problems pertaining to fluid mechanics
76M99	Basic methods in fluid mechanics

Keywords:

finite-element discretization; Stokes problem; bounded domain; conjugate- gradient algorithm; two discrete Poisson equations; convergence rate