Numerical Treatment of the Navier-Stokes Equations

Wolfgang Hackbusch,Rolf Rannacher

Numerical Treatment of the Navier-Stokes Equations
Format
Hardback
Publisher
Friedrich Vieweg & Sohn Verlagsgesellschaft mbH
Country
Germany
Published
11 April 1991
Pages
174
ISBN
9783528076306

Numerical Treatment of the Navier-Stokes Equations

Wolfgang Hackbusch,Rolf Rannacher

This title is printed to order. This book may have been self-published. If so, we cannot guarantee the quality of the content. In the main most books will have gone through the editing process however some may not. We therefore suggest that you be aware of this before ordering this book. If in doubt check either the author or publisher’s details as we are unable to accept any returns unless they are faulty. Please contact us if you have any questions.

The most frequently used method for the numerical integration of parabolic differential equa- tions is the method of lines, where one first uses a discretization of space derivatives by finite differences or finite elements and then uses some time-stepping method for the the solution of resulting system of ordinary differential equations. Such methods are, at least conceptually, easy to perform. However, they can be expensive if steep gradients occur in the solution, stability must be controlled, and the global error control can be troublesome. This paper considers a simultaneaus discretization of space and time variables for a one-dimensional parabolic equation on a relatively long time interval, called ‘time-slab’. The discretization is repeated or adjusted for following ‘time-slabs’ using continuous finite element approximations. In such a method we utilize the efficiency of finite elements by choosing a finite element mesh in the time-space domain where the finite element mesh has been adjusted to steep gradients of the solution both with respect to the space and the time variables. In this way we solve all the difficulties with the classical approach since stability, discretization error estimates and global error control are automatically satisfied. Such a method has been discussed previously in [3] and [4]. The related boundary value techniques or global time integration for systems of ordinary differential equations have been discussed in several papers, see [12] and the references quoted therein.

This item is not currently in-stock. It can be ordered online and is expected to ship in 7-14 days

Our stock data is updated periodically, and availability may change throughout the day for in-demand items. Please call the relevant shop for the most current stock information. Prices are subject to change without notice.

Sign in or become a Readings Member to add this title to a wishlist.