Generalities on Elliptic Variational Inequalities and on Their Approximation.- Application of the Finite Element Method to the Approximation of Some Second-Order EVI.- On the Approximation of Parabolic Variational Inequalities.- Applications of Elliptic Variational Inequality Methods to the Solution of Some Nonlinear Elliptic Equations.- Relaxation Methods and Applications.- Decomposition-Coordination Methods by Augmented Lagrangian: Applications.- Least-Squares Solution of Nonlinear Problems: Application to Nonlinear Problems in Fluid Dynamics.
When Herb Keller suggested, more than two years ago, that we update our lectures held at the Tata Institute of Fundamental Research in 1977, and then have it published in the collection Springer Series in Computational Physics, we thought, at first, that it would be an easy task. Actually, we realized very quickly that it would be more complicated than what it seemed at first glance, for several reasons: 1. The first version of Numerical Methods for Nonlinear Variational Problems was, in fact, part of a set of monographs on numerical mat- matics published, in a short span of time, by the Tata Institute of Fun- mental Research in its well-known series Lectures on Mathematics and Physics; as might be expected, the first version systematically used the material of the above monographs, this being particularly true for Lectures on the Finite Element Method by P. G. Ciarlet and Lectures on Optimization—Theory and Algorithms by J. Cea. This second version had to be more self-contained. This necessity led to some minor additions in Chapters I-IV of the original version, and to the introduction of a chapter (namely, Chapter Y of this book) on relaxation methods, since these methods play an important role in various parts of this book.
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