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1 
NavierStokes equations as a differentialalgebraic systemWeickert, J. 30 October 1998 (has links) (PDF)
Nonsteady NavierStokes equations represent a differentialalgebraic system of strangeness index one after any spatial discretization. Since such systems are hard to treat in their original form, most approaches use some kind of index reduction. Processing this index reduction it is important to take care of the manifolds contained in the differentialalgebraic equation (DAE). We investigate for several discretization schemes for the NavierStokes equations how the consideration of the manifolds is taken into account and propose a variant of solving these equations along the lines of the theoretically best index reduction. Applying this technique, the error of the time discretisation depends only on the method applied for solving the DAE.

2 
NavierStokes equations as a differentialalgebraic systemWeickert, J. 30 October 1998 (has links)
Nonsteady NavierStokes equations represent a differentialalgebraic system of strangeness index one after any spatial discretization. Since such systems are hard to treat in their original form, most approaches use some kind of index reduction. Processing this index reduction it is important to take care of the manifolds contained in the differentialalgebraic equation (DAE). We investigate for several discretization schemes for the NavierStokes equations how the consideration of the manifolds is taken into account and propose a variant of solving these equations along the lines of the theoretically best index reduction. Applying this technique, the error of the time discretisation depends only on the method applied for solving the DAE.

3 
Tauextrapolation  theoretische Grundlagen, numerische Experimente und Anwendungen auf die NavierStokesGleichungenBernert, K. 30 October 1998 (has links) (PDF)
The paper deals with tauextrapolation  a modification of the
multigrid method, which leads to solutions with an improved con
vergence order. The number of numerical operations depends
linearly on the problem size and is not much higher than for a
multigrid method without this modification. The paper starts
with a short mathematical foundation of the tauextrapolation.
Then follows a careful tuning of some multigrid components
necessary for a successful application of tauextrapolation. The
next part of the paper presents numerical illustrations to the
theoretical investigations for one dimensional test problems.
Finally some experience with the use of tauextrapolation for the
NavierStokes equations is given.

4 
Tauextrapolation  theoretische Grundlagen, numerische Experimente und Anwendungen auf die NavierStokesGleichungenBernert, K. 30 October 1998 (has links)
The paper deals with tauextrapolation  a modification of the
multigrid method, which leads to solutions with an improved con
vergence order. The number of numerical operations depends
linearly on the problem size and is not much higher than for a
multigrid method without this modification. The paper starts
with a short mathematical foundation of the tauextrapolation.
Then follows a careful tuning of some multigrid components
necessary for a successful application of tauextrapolation. The
next part of the paper presents numerical illustrations to the
theoretical investigations for one dimensional test problems.
Finally some experience with the use of tauextrapolation for the
NavierStokes equations is given.

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