Numerical Methods for Nonlinear Variational Problems / Edition 1 available in Hardcover
- Pub. Date:
- Springer-Verlag New York, LLC
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, and nonlinear least square methods are all covered in detail, as are many applications. This volume is a classic in a long-awaited softcover re-edition.
Table of Contents
I Generalities on Elliptic Variational Inequalities and on Their Approximation.- II Application of the Finite Element Method to the Approximation of Some Second-Order EVI.- III On the Approximation of Parabolic Variational Inequalities.- IV Applications of Elliptic Variational Inequality Methods to the Solution of Some Nonlinear Elliptic Equations.- V Relaxation Methods and Applications.- VI Decomposition-Coordination Methods by Augmented Lagrangian: Applications.- VII Least-Squares Solution of Nonlinear Problems: Application to Nonlinear Problems in Fluid Dynamics.- Appendix I A Brief Introduction to Linear Variational Problems.- 1. Introduction.- 2. A Family of Linear Variational Problems.- 3. Internal Approximation of Problem (P).- 4. Application to the Solution of Elliptic Problems for Partial Differential Operators.- 5. Further Comments: Conclusion.- Appendix II A Finite Element Method with Upwinding for Second-Order Problems with Large First Order Terms.- 1. Introduction.- 2. The Model Problem.- 3. A Centered Finite Element Approximation.- 4. A Finite Element Approximation with Upwinding.- 5. On the Solution of the Linear System Obtained by Upwinding.- 6. Numerical Experiments.- 7. Concluding Comments.- Appendix III Some Complements on the Navier-Stokes Equations and Their Numerical Treatment.- 1. Introduction.- 4. Further Comments on the Boundary Conditions.- 5. Decomposition Properties of the Continuous and Discrete Stokes Problems of Sec. 4. Application to Their Numerical Solution.- 6. Further Comments.- Some Illustrations from an Industrial Application.- Glossary of Symbols.- Author Index.