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Partial differential equations /
$81.1\x$a /homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! Over the second half of the 20th century the subject area loosely referred to as numerical analysis of partial differential equations (PDEs) has undergone unprecedented development. At its practical end, t...
| Clasificación: | Libro Electrónico |
|---|---|
| Otros Autores: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Amsterdam ; New York :
Elsevier,
2001.
|
| Edición: | 1st ed. |
| Colección: | Numerical analysis 2000 ;
v. 7. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Partial Differential Equations; Copyright Page; Table of Contents; Preface; Chapter 1. From finite differences to finite elements. A short history of numerical analysis of partial differential equations; Abstract; 0. Introduction; 1. The Courant-Friedrichs-Lewy paper; 2. Finite difference methods for elliptic problems; 3. Finite difference methods for initial value problems; 4. Finite differences for mixed initial-boundary value problems; 5. Finite element methods for elliptic problems; 6. Finite element methods for evolution equations
- 7. Some other classes of approximation methods8. Numerical linear algebra for elliptic problems; References; Survey articles and books; Chapter 2. Orthogonal spline collocation methods for partial differential equations; Abstract; 1. Introduction; 2. Problems in one space variable; 3. Elliptic boundary value problems; 4. Time-dependent problems; 5. Modified spline collocation methods; Acknowledgements; References; Chapter 3. Spectral methods for hyperbolic problems; Abstract; 1. Introduction; 2. Modes and nodes; 3. Approximation results; 4. Collocation approximations of hyperbolic problems
- 5. Stability results for hyperbolic problems6. Convergence results for nonlinear hyperbolic problems; 7. Multi-domain methods; 8. A few applications and concluding remarks; References; Chapter 4. Wavelet methods for PDEs
- some recent developments; Abstract; 1. Introduction; 2. Some preliminary comments; 3. The key features; 4. Well-posedness in Euclidean metric; 5. Near sparsity of matrix representations; 6. Adaptive wavelet schemes; 7. Nonlinear problems; 8. About the tools
- some basic concepts; 9. Construction of wavelets on bounded domains
- 10. Applications in conventional discretizations11. Concluding remarks; References; Chapter 5. Devising discontinuous Galerkin methods for non-linear hyperbolic conservation laws; Abstract; 1. Introduction; 2. The main difficulty: the loss of well-posedness; 3. Devising discontinuous Galerkin methods: heuristics; 4. The RKDG method; 5. Concluding remarks; Acknowledgements; References; Chapter 6. Adaptive Galerkin finite element methods for partial differential equations; Abstract; 1. Introduction; 2. A general paradigm for a posteriori error estimation
- 3. Evaluation of the a posteriori error estimates4. Algorithmic aspects of mesh adaptation; 5. A nested solution approach; 6. Applications to model problems; 7. Conclusion and outlook; Acknowledgements; References; Chapter 7. The p and hp finite element method for problems on thin domains; Abstract; 1. Introduction; 2. h, p and hp finite element spaces; 3. Control of modeling error; 4. Approximation of singularities; 5. Resolution of boundary layers; 6. The problem of locking; References; Chapter 8. Efficient preconditioning of the linearized Navier-Stokes equations for incompressible flow