内容

目次

1. Examples and classification of PDEs; 2. The maximum principle; 3.Finite difference methods; 4. A convergence theory for differencemethods; 5. Sobolev spaces; 6. Variational formulation of ellipticboundary-value problems of second order; 7. The Neumann boundary-valueproblem; 8. The Ritz-Galerkin method and simple finite elements; 9.Some standard finite elements; 10. Approximation properties; 11. Errorbounds for elliptic problems of second order; 12. Computationalconsiderations; 13. Abstract lemmas and a simple boundaryapproximation; 14. Isoperimetric elements; 15. Further tools fromfunctional analysis; 16. Saddle point problems; 17. Stokes' equation;18. Finite elements for the Stokes problem; 19. A posteriori errorestimates; 20. Classical iterative methods for solving linear systems;21. Gradient methods; 22. Conjugate gradient and minimal residualmethods; 23. Preconditioning; 24. Saddle point problems; 25. Multigridmethods for variational problems; 26. Convergence of multigrid methods;27. Convergence for several levels; 28. Nested iteration; 29. Nonlinearproblems; 30. Introduction to elasticity; 31. Hyperelastic problems;32. Linear elasticity theory; 33. Membranes; 34. Beams and plates: theKirchhoff Plate; 35. The Mindlin-Reissner Plate.