04355cam a22004575i 4500
BYT
130503s1984 gw | s |||| 0|eng d
9783662126158
eng
23
518.6
Glowinski, Roland.
2707
Numerical methods for nonlinear variational problems /
by Roland Glowinski.
New York :
Springer-Verlag,
c1984
xiii, 493 pages :
illustrations ;
24 cm.
Springer Series in Computational Physics,
1434-8322
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.
Many 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.
Physics
432
Física
102
Computer science
Mathematics.
133
Ciencia de la computación
Matemáticas
2402
Mathematical optimization.
Engineering mathematics.
Matemáticas de ingeniería.
2708
Engineering.
Physics.
Numerical and Computational Physics.
2709
Física Numérica y Computacional
2710
Computational Intelligence.
2711
Inteligencia artificial
2298
Computational Mathematics and Numerical Analysis.
2712
Matemáticas computacionales y análisis numérico.
2713
Classical Continuum Physics.
2714
Física Continua Clásica
2715
Appl.Mathematics/Computational Methods of Engineering.
2716
Aplicaciones matemáticas
2717
Calculus of Variations and Optimal Control; Optimization.
2718
Cálculo de variaciones y control óptimo
2719
Optimización
Springer Series in Computational Physics
2720
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