Numerical Methods for Nonlinear Variational ProblemsMany mechanics and physics problems have variational formulations making them appropriate for numerical treatment by finite element techniques and efficient iterative methods. This book describes the mathematical background and reviews the techniques for solving problems, including those that require large computations such as transonic flows for compressible fluids and the Navier-Stokes equations for incompressible viscous fluids. Finite element approximations and non-linear relaxation, augmented Lagrangians, and nonlinear least square methods are all covered in detail, as are many applications. "Numerical Methods for Nonlinear Variational Problems", originally published in the Springer Series in Computational Physics, is a classic in applied mathematics and computational physics and engineering. This long-awaited softcover re-edition is still a valuable resource for practitioners in industry and physics and for advanced students. |
Contents
5 | |
12 | |
Application of the Finite Element Method to the Approximation | 27 |
The ElastoPlastic Torsion | 41 |
A Simplified Signorini Problem | 56 |
A Simplified Friction Problem | 68 |
The Flow of a Viscous | 78 |
On Some Useful Formulae | 96 |
Applications | 194 |
Transonic Flow Calculations by LeastSquares and Finite Element Methods | 211 |
Numerical Solution of the NavierStokes Equations for Incompressible | 244 |
Further Comments on Chapter VII and Conclusion | 318 |
APPENDIX I | 321 |
Application to the Solution of Elliptic Problems for Partial Differential | 330 |
179 | 362 |
211 | 368 |
Approximation of PVI of the Second Kind | 103 |
CHAPTER IV | 110 |
78 | 123 |
Theoretical and Numerical Analysis of Some Mildly Nonlinear Elliptic | 129 |
CHAPTER V | 140 |
Block Relaxation Methods | 151 |
Solution of Systems of Nonlinear Equations by Relaxation Methods | 163 |
Description of the Algorithms | 170 |
Convergence of ALG 2 | 177 |
Conclusion | 397 |
On the Solution of the Linear System Obtained by Upwinding | 404 |
Concluding Comments | 414 |
Decomposition Properties of the Continuous and Discrete Stokes Problems | 425 |
Some Illustrations from an Industrial Application | 431 |
Glossary of Symbols 455 | 454 |
463 | |