Finite Elements
Theory, Fast Solvers, and Applications in Solid Mechanics
Published on 8. May 1997
Book
Hardback
339 pages
978-0-521-58187-5 (ISBN)
Description
The most important application of the finite element method is the numerical solution of elliptical partial differential equations. This is covered in depth in this book. It is a textbook for graduate students who do not necessarily have any particular background in differential equations, but require an introduction to finite elements for engineering or mathematics applications.
Reviews / Votes
'This is a well-written book on the mathematical foundation of the finite element method which should appeal to graduate mathematicians and researchers in numerical methods and theoretical mechanics. The coveraGE OF THE MATHEMATICAL THEORIES USED IN THE FINITE ELEMENT FORMULATION IS COMPREHENSIVE.' A. A. Becker, Journal of Mechanical Engineering Science ' ... this is an excellent book that is appealing to both mathematicians and engineers'. N Herrmann, Zentralblatt fuer Mathematik und ihre Grenzgebiete 'The book is well suited as a student's textbook in an introductory finite element class, but also for the lecturer himself for designing such courses ... Readers with interest in time dependent problems, in the treatment of nonlinear elliptic partial differential equations, or those which are more interested in practical implementation, obtain in this book a solid theoretical foundation. The book is highly recommended.' H. Blum, University of DortmundMore details
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Dimensions
Height: 236 mm
Width: 157 mm
Thickness: 23 mm
Weight
570 gr
ISBN-13
978-0-521-58187-5 (9780521581875)
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Schweitzer Classification
Other editions
New editions
Book
04/2007
3rd Edition
Cambridge University Press
€90.40
Shipment within 15-20 days
Persons
Content
1. Examples and classification of PDEs; 2. The maximum principle; 3. Finite difference methods; 4. A convergence theory for difference methods; 5. Sobolev spaces; 6. Variational formulation of elliptic boundary-value problems of second order; 7. The Neumann boundary-value problem; 8. The Ritz-Galerkin method and simple finite elements; 9. Some standard finite elements; 10. Approximation properties; 11. Error bounds for elliptic problems of second order; 12. Computational considerations; 13. Abstract lemmas and a simple boundary approximation; 14. Isoperimetric elements; 15. Further tools from functional analysis; 16. Saddle point problems; 17. Stokes' equation; 18. Finite elements for the Stokes problem; 19. A posteriori error estimates; 20. Classical iterative methods for solving linear systems; 21. Gradient methods; 22. Conjugate gradient and minimal residual methods; 23. Preconditioning; 24. Saddle point problems; 25. Multigrid methods for variational problems; 26. Convergence of multigrid methods; 27. Convergence for several levels; 28. Nested iteration; 29. Nonlinear problems; 30. Introduction to elasticity; 31. Hyperelastic problems; 32. Linear elasticity theory; 33. Membranes; 34. Beams and plates: the Kirchhoff Plate; 35. The Mindlin-Reissner Plate.