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.

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.