Numerical methods for nonlinear variational problems
Glowinski, Roland.
creator
text
gw
1984
First Edition
monographic
eng
xiii, 493 pages : illustrations ; 24 cm.
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.
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.
by Roland Glowinski.
Physics
Física
Computer science
Mathematics
Ciencia de la computación
Matemáticas
Mathematical optimization
Engineering mathematics
Matemáticas de ingeniería
Engineering
Physics
Numerical and Computational Physics
Física Numérica y Computacional
Computational Intelligence
Inteligencia artificial
Computational Mathematics and Numerical Analysis
Matemáticas computacionales y análisis numérico
Classical Continuum Physics
Física Continua Clásica
Appl.Mathematics/Computational Methods of Engineering
Aplicaciones matemáticas
Calculus of Variations and Optimal Control; Optimization
Cálculo de variaciones y control óptimo
Optimización
518.6 G5669n 1984
Springer Series in Computational Physics
Springer Series in Computational Physics
9783662126158
EC-UrYT
130503
20210827130231.0