Finite elements : theory, fast solvers, and applications in solid mechanics
Dietrich Braess ; translated by Larry L. Schumaker.
Cambridge, U.K. : Cambridge University Press, 1997.
xvi, 323 págs. : ilustraciones ; 23 cm.
ISBN: 0521588340 (pbk.), 0521581877
Traducción revisada de: Finite Elemente. Berlin : Springer, 1992.
Incluye referencias bibliográficas (p. 309-318) e índice.
Reseña: MathSciNet, 98f:65002
Contenido
- 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.
