Numerical Methods for Nonlinear Variational Problems

Roland Glowinski (auth.)978-3-540-77506-5

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.

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Table of contents :

Content:
Front Matter….Pages i-xv
Generalities on Elliptic Variational Inequalities and on Their Approximation….Pages 1-26
Application of the Finite Element Method to the Approximation of Some Second-Order EVI….Pages 27-97
On the Approximation of Parabolic Variational Inequalities….Pages 98-109
Applications of Elliptic Variational Inequality Methods to the Solution of Some Nonlinear Elliptic Equations….Pages 110-139
Relaxation Methods and Applications….Pages 140-165
Decomposition-Coordination Methods by Augmented Lagrangian: Applications….Pages 166-194
Least-Squares Solution of Nonlinear Problems: Application to Nonlinear Problems in Fluid Dynamics….Pages 195-320
Back Matter….Pages 321-493