Finite elements : theory, fast solvers, and applications in solid mechanics / Dietrich Braess ; translated by Larry L. Schumaker.
Idioma: Inglés Lenguaje original: Alemán Editor: Cambridge, U.K. : Cambridge University Press, 1997Descripción: xvi, 323 p. : il. ; 23 cmISBN: 0521588340 (pbk.); 0521581877Títulos uniformes: Finite Elemente. Inglés Tema(s): Finite element method | Elasticity -- Mathematical modelsOtra clasificación: 65-02 (65-01 65M60 65N30 74S05) Recursos en línea: Publisher description1. Examples and classification of PDEs2. The maximum principle3. Finite difference methods4. A convergence theory for difference methods5. Sobolev spaces6. Variational formulation of elliptic boundary-value problems of second order7. The Neumann boundary-value problem8. The Ritz-Galerkin method and simple finite elements9. Some standard finite elements10. Approximation properties11. Error bounds for elliptic problems of second order12. Computational considerations13. Abstract lemmas and a simple boundary approximation14. Isoperimetric elements15. Further tools from functional analysis16. Saddle point problems17. Stokes' equation18. Finite elements for the Stokes problem19. A posteriori error estimates20. Classical iterative methods for solving linear systems21. Gradient methods22. Conjugate gradient and minimal residual methods23. Preconditioning24. Saddle point problems25. Multigrid methods for variational problems26. Convergence of multigrid methods27. Convergence for several levels28. Nested iteration29. Nonlinear problems30. Introduction to elasticity31. Hyperelastic problems32. Linear elasticity theory33. Membranes34. Beams and plates: the Kirchhoff Plate35. The Mindlin-Reissner Plate.
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Traducción revisada de: Finite Elemente. Berlin : Springer, 1992.
Incluye referencias bibliográficas (p. 309-318) e índice.
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.
MR, 98f:65002
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