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Author : Vivette Girault,Pierre-Arnaud Raviart
Publisher : Springer
Page : 222 pages
File Size : 49,8 Mb
Release : 1979
Category : Finite element method
ISBN : STANFORD:36105031465961
Author : Vivette Girault,P. A. Raviart
Publisher : Unknown
Page : 220 pages
File Size : 52,8 Mb
Release : 2014-09-01
Category : Electronic
ISBN : 3662197359
Author : Vivette Girault,P.-A. Raviart
Publisher : Springer Verlag
Page : 199 pages
File Size : 53,7 Mb
Release : 1981-01-01
Category : Mathematics
ISBN : 3540095578
Author : Vivette Girault,Pierre-Arnaud Raviart
Publisher : Springer Science & Business Media
Page : 386 pages
File Size : 51,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642616235
The material covered by this book has been taught by one of the authors in a post-graduate course on Numerical Analysis at the University Pierre et Marie Curie of Paris. It is an extended version of a previous text (cf. Girault & Raviart [32J) published in 1979 by Springer-Verlag in its series: Lecture Notes in Mathematics. In the last decade, many engineers and mathematicians have concentrated their efforts on the finite element solution of the Navier-Stokes equations for incompressible flows. The purpose of this book is to provide a fairly comprehen sive treatment of the most recent developments in that field. To stay within reasonable bounds, we have restricted ourselves to the case of stationary prob lems although the time-dependent problems are of fundamental importance. This topic is currently evolving rapidly and we feel that it deserves to be covered by another specialized monograph. We have tried, to the best of our ability, to present a fairly exhaustive treatment of the finite element methods for inner flows. On the other hand however, we have entirely left out the subject of exterior problems which involve radically different techniques, both from a theoretical and from a practical point of view. Also, we have neither discussed the implemen tation of the finite element methods presented by this book, nor given any explicit numerical result. This field is extensively covered by Peyret & Taylor [64J and Thomasset [82].
Author : F. Thomasset
Publisher : Springer Science & Business Media
Page : 168 pages
File Size : 45,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642870477
In structure mechanics analysis, finite element methods are now well estab lished and well documented techniques; their advantage lies in a higher flexibility, in particular for: (i) The representation of arbitrary complicated boundaries; (ii) Systematic rules for the developments of stable numerical schemes ap proximating mathematically wellposed problems, with various types of boundary conditions. On the other hand, compared to finite difference methods, this flexibility is paid by: an increased programming complexity; additional storage require ment. The application of finite element methods to fluid mechanics has been lagging behind and is relatively recent for several types of reasons: (i) Historical reasons: the early methods were invented by engineers for the analysis of torsion, flexion deformation of bearns, plates, shells, etc ... (see the historics in Strang and Fix (1972) or Zienckiewicz (1977». (ii) Technical reasons: fluid flow problems present specific difficulties: strong gradients,l of the velocity or temperature for instance, may occur which a finite mesh is unable to properly represent; a remedy lies in the various upwind finite element schemes which recently turned up, and which are reviewed in chapter 2 (yet their effect is just as controversial as in finite differences). Next, waves can propagate (e.g. in ocean dynamics with shallowwaters equations) which will be falsely distorted by a finite non regular mesh, as Kreiss (1979) pointed out. We are concerned in this course with the approximation of incompressible, viscous, Newtonian fluids, i.e. governed by N avier Stokes equations.
Author : C. Cuvelier,A. Segal,A.A. van Steenhoven
Publisher : Springer Science & Business Media
Page : 504 pages
File Size : 51,8 Mb
Release : 1986-03-31
Category : Computers
ISBN : 9789027721488
Author : Cedric Taylor,T. G. Hughes
Publisher : Unknown
Page : 264 pages
File Size : 49,8 Mb
Release : 1981
Category : Mathematics
ISBN : STANFORD:36105030610054
Author : Volker John
Publisher : Springer
Page : 812 pages
File Size : 49,6 Mb
Release : 2016-10-27
Category : Mathematics
ISBN : 9783319457505
This book explores finite element methods for incompressible flow problems: Stokes equations, stationary Navier-Stokes equations and time-dependent Navier-Stokes equations. It focuses on numerical analysis, but also discusses the practical use of these methods and includes numerical illustrations. It also provides a comprehensive overview of analytical results for turbulence models. The proofs are presented step by step, allowing readers to more easily understand the analytical techniques.
Author : Howard C. Elman,David J. Silvester,Andrew J. Wathen
Publisher : Unknown
Page : 495 pages
File Size : 52,6 Mb
Release : 2014
Category : Mathematics
ISBN : 9780199678808
This book describes why and how to do Scientific Computing for fundamental models of fluid flow. It contains introduction, motivation, analysis, and algorithms and is closely tied to freely available MATLAB codes that implement the methods described. The focus is on finite element approximation methods and fast iterative solution methods for the consequent linear(ized) systems arising in important problems that model incompressible fluid flow. The problems addressed are the Poisson equation, Convection-Diffusion problem, Stokes problem and Navier-Stokes problem, including new material on time-dependent problems and models of multi-physics. The corresponding iterative algebra based on preconditioned Krylov subspace and multigrid techniques is for symmetric and positive definite, nonsymmetric positive definite, symmetric indefinite and nonsymmetric indefinite matrix systems respectively. For each problem and associated solvers there is a description of how to compute together with theoretical analysis that guides the choice of approaches and describes what happens in practice in the many illustrative numerical results throughout the book (computed with the freely downloadable IFISS software). All of the numerical results should be reproducible by readers who have access to MATLAB and there is considerable scope for experimentation in the "computational laboratory" provided by the software. Developments in the field since the first edition was published have been represented in three new chapters covering optimization with PDE constraints (Chapter 5); solution of unsteady Navier-Stokes equations (Chapter 10); solution of models of buoyancy-driven flow (Chapter 11). Each chapter has many theoretical problems and practical computer exercises that involve the use of the IFISS software. This book is suitable as an introduction to iterative linear solvers or more generally as a model of Scientific Computing at an advanced undergraduate or beginning graduate level.
Author : Cornelis Cuvelier,August Segal,Anton A. Steenhoven
Publisher : Unknown
Page : 0 pages
File Size : 44,9 Mb
Release : 1986
Category : Finite element method
ISBN : OCLC:1348974991
Author : Hou-Cheng Huang,Zheng-Hua Li,Asif S. Usmani
Publisher : Springer Science & Business Media
Page : 225 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781447107996
A follow on from the author's work "Finite Elements in Heat Transfer" which we published 11/94, and which is a powerful CFD programme that will run on a PC. The fluid flow market is larger than the previous, and this package is good value in comparison with other software packages in Computational Fluid Dynamics, which are generally very expensive. The work in general copes with non-Newtonian laminar flow using the finite element method, and some basic theory of the subject is included in the opening chapters of the book.
Author : Wolfgang Bangerth,Rolf Rannacher
Publisher : Birkhäuser
Page : 216 pages
File Size : 43,5 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9783034876056
These Lecture Notes have been compiled from the material presented by the second author in a lecture series ('Nachdiplomvorlesung') at the Department of Mathematics of the ETH Zurich during the summer term 2002. Concepts of 'self adaptivity' in the numerical solution of differential equations are discussed with emphasis on Galerkin finite element methods. The key issues are a posteriori er ror estimation and automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method (or shortly D WR method) for goal-oriented error estimation is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. 'Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. The basics of the DWR method and various of its applications are described in the following survey articles: R. Rannacher [114], Error control in finite element computations. In: Proc. of Summer School Error Control and Adaptivity in Scientific Computing (H. Bulgak and C. Zenger, eds), pp. 247-278. Kluwer Academic Publishers, 1998. M. Braack and R. Rannacher [42], Adaptive finite element methods for low Mach-number flows with chemical reactions.
Author : Jean Donea,Antonio Huerta
Publisher : John Wiley & Sons
Page : 366 pages
File Size : 48,5 Mb
Release : 2003-06-02
Category : Science
ISBN : 0471496669
Die Finite-Elemente-Methode, eines der wichtigsten in der Technik verwendeten numerischen Näherungsverfahren, wird hier gründlich und gut verständlich, aber ohne ein Zuviel an mathematischem Formalismus abgehandelt. Insbesondere geht es um die Anwendung der Methode auf Strömungsprobleme. Alle wesentlichen aktuellen Forschungsergebnisse wurden in den Band aufgenommen; viele davon sind bisher nur verstreut in der Originalliteratur zu finden.
Author : O. C. Zienkiewicz,K. Morgan
Publisher : Courier Corporation
Page : 356 pages
File Size : 42,9 Mb
Release : 2013-04-22
Category : Technology & Engineering
ISBN : 9780486318011
A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises. Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher order finite element approximation, mapping and numerical integration, variational methods, and partial discretization and time-dependent problems. A survey of generalized finite elements and error estimates concludes the text.
Author : R. Rautmann
Publisher : Springer
Page : 602 pages
File Size : 46,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540385509
