Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics - Brossura

Braess, Dietrich

Brossura

ISBN 10: 0521588340 ISBN 13: 9780521588348

Casa editrice: Cambridge University Press, 1997

Riassunto

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.

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Recensione

'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 für 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 Dortmund

Contenuti

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.

Dettagli dell?edizione

• Editore: Cambridge University Press
• Data di pubblicazione: 1997
• ISBN 10: 0521588340
• ISBN 13: 9780521588348
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero di pagine: 339