Tauextrapolation - theoretische Grundlagen, numerische Experimente und Anwendungen auf die Navier-Stokes-Gleichungen

• Main Author: Bernert, K.
• Language: German
• Published: Technische Universität Chemnitz 1998
• Subjects: info:eu-repo/classification/ddc/510; ddc:510; linear problems; nonlinear problems; improved convergence; one-dimensional test; MSC 76M20; MSC 65N55; MSC 76D05
• Online Access: http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800506; https://monarch.qucosa.de/id/qucosa%3A17423; https://monarch.qucosa.de/api/qucosa%3A17423/attachment/ATT-0/; https://monarch.qucosa.de/api/qucosa%3A17423/attachment/ATT-1/; https://monarch.qucosa.de/api/qucosa%3A17423/attachment/ATT-2/

The paper deals with tau-extrapolation - 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 tau-extrapolation. Then follows a careful tuning of some multigrid components necessary for a successful application of tau-extrapolation. 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 tau-extrapolation for the Navier-Stokes equations is given.