Variational Methods for the Numerical Solution of Nonlinear Elliptic Problems (CBMS-NSF Regional Conference Series in Applied Mathematics, Series Number 86)

Variational Methods for the Numerical Solution of Nonlinear Elliptic Problems addresses computational methods that have proven efficient for the solution of a large variety of nonlinear elliptic problems. These methods can be applied to many problems in science and engineering, but this book focuses on their application to problems in continuum mechanics and physics.

This book differs from others on the topic by presenting examples of the power and versatility of operator-splitting methods; providing a detailed introduction to alternating direction methods of multipliers and their applicability to the solution of nonlinear (possibly nonsmooth) problems from science and engineering; and showing that nonlinear least-squares methods, combined with operator-splitting and conjugate gradient algorithms, provide efficient tools for the solution of highly nonlinear problems.

Audience: The book provides useful insights suitable for advanced graduate students, faculty, and researchers in applied and computational mathematics as well as research engineers, mathematical physicists, and systems engineers.

Contents: Preface; Chapter 1: On some variational problems in Hilbert spaces; Chapter 2: Iterative methods in Hilbert spaces; Chapter 3: Operator-splitting and alternating direction methods; Chapter 4: Augmented Lagrangians and alternating direction methods of multipliers; Chapter 5: Least-squares solution of linear and nonlinear problems in Hilbert spaces; Chapter 6: Obstacle problems and Bingham flow application to control; Chapter 7: Other nonlinear eigenvalue problems; Chapter 8: Eikonal equations; Chapter 9: Fully nonlinear elliptic problems; Epilogue; Bibliography; Author index; Subject index.