| Some Preliminary Comments | p. xiv |
| Generalities on Elliptic Variational Inequalities and on Their Approximation | p. 1 |
| Introduction | p. 1 |
| Functional Context | p. 1 |
| Existence and Uniqueness Results for EVI of the First Kind | p. 3 |
| Existence and Uniqueness Results for EVI of the Second Kind | p. 5 |
| Internal Approximation of EVI of the First Kind | p. 8 |
| Internal Approximation of EVI of the Second Kind | p. 12 |
| Penalty Solution of Elliptic Variational Inequalities of the First Kind | p. 15 |
| References | p. 26 |
| Application of the Finite Element Method to the Approximation of Some Second-Order EVI | p. 27 |
| Introduction | p. 27 |
| An Example of EVI of the First Kind: The Obstacle Problem | p. 27 |
| A Second Example of EVI of the First Kind: The Elasto-Plastic Torsion Problem | p. 41 |
| A Third Example of EVI of the First Kind: A Simplified Signorini Problem | p. 56 |
| An Example of EVI of the Second Kind: A Simplified Friction Problem | p. 68 |
| A Second Example of EVI of the Second Kind: The Flow of a Viscous Plastic Fluid in a Pipe | p. 78 |
| On Some Useful Formulae | p. 96 |
| On the Approximation of Parabolic Variational Inequalities | p. 98 |
| Introduction: References | p. 98 |
| Formulation and Statement of the Main Results | p. 98 |
| Numerical Schemes for Parabolic Linear Equations | p. 99 |
| Approximation of PVI of the First Kind | p. 101 |
| Approximation of PVI of the Second Kind | p. 103 |
| Application to a Specific Example: Time-Dependent Flow of a Bingham Fluid in a Cylindrical Pipe | p. 104 |
| Applications of Elliptic Variational Inequality Methods to the Solution of Some Nonlinear Elliptic Equations | p. 110 |
| Introduction | p. 110 |
| Theoretical and Numerical Analysis of Some Mildly Nonlinear Elliptic Equations | p. 110 |
| A Subsonic Flow Problem | p. 134 |
| Relaxation Methods and Applications | p. 140 |
| Generalities | p. 140 |
| Some Basic Results of Convex Analysis | p. 140 |
| Relaxation Methods for Convex Functionals: Finite-Dimensional Case | p. 142 |
| Block Relaxation Methods | p. 151 |
| Constrained Minimization of Quadratic Functionals in Hilbert Spaces by Under and Over-Relaxation Methods: Application | p. 152 |
| Solution of Systems of Nonlinear Equations by Relaxation Methods | p. 163 |
| Decomposition-Coordination Methods by Augmented Lagrangian: Applications | p. 166 |
| Introduction | p. 166 |
| Properties of (P) and of the Saddle Points of <$>{scr L}<$> and <$>{scr L}_r<$> | p. 168 |
| Description of the Algorithms | p. 170 |
| Convergence of ALG 1 | p. 171 |
| Convergence of ALG 2 | p. 179 |
| Applications | p. 183 |
| General Comments | p. 194 |
| Least-Squares Solution of Nonlinear Problems: Application to Nonlinear Problems in Fluid Dynamics | p. 195 |
| Introduction: Synopsis | p. 195 |
| Least-Squares Solution of Finite-Dimensional Systems of Equations | p. 195 |
| Least-Squares Solution of a Nonlinear Dirichlet Model Problem | p. 198 |
| Transonic Flow Calculations by Least-Squares and Finite Element Methods | p. 211 |
| Numerical Solution of the Navier-Stokes Equations for Incompressible Viscous Fluids by Least-Squares and Finite Element Methods | p. 244 |
| Further Comments on Chapter VII and Conclusion | p. 318 |
| A Brief Introduction to Linear Variational Problems | p. 321 |
| Introduction | p. 321 |
| A Family of Linear Variational Problems | p. 321 |
| Internal Approximation of Problem (P) | p. 326 |
| Application to the Solution of Elliptic Problems for Partial Differential Operators | p. 330 |
| Further Comments: Conclusion | p. 397 |
| A Finite Element Method with Upwinding for Second-Order Problems with Large First- Order Terms | p. 399 |
| Introduction | p. 399 |
| The Model Problem | p. 399 |
| A Centered Finite Element Approximation | p. 400 |
| A Finite Element Approximation with Upwinding | p. 400 |
| On the Solution of the Linear System Obtained by Upwinding | p. 404 |
| Numerical Experiments | p. 404 |
| Concluding Comments | p. 414 |
| Some Complements on the Navier-Stokes Equations and Their Numerical Treatment | p. 415 |
| Introduction | p. 415 |
| Finite Element Approximation of the Boundary Condition u = g on ¿ if g &neq; 0 | p. 415 |
| Some Comments On the Numerical Treatment of the Nonlinear Term (u · ∇)u | p. 416 |
| Further Comments on the Boundary Conditions | p. 417 |
| Decomposition Properties of the Continuous and Discrete Stokes Problems of Sec. 4. Application to Their Numerical Solution | p. 425 |
| Further Comments | p. 430 |
| Some Illustrations from an Industrial Application | p. 431 |
| Bibliography | p. 435 |
| Glossary of Symbols | p. 455 |
| Author Index | p. 463 |
| Subject Index | p. 467 |
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