Variational Methods for the Numerical Solution of Nonlinear Elliptic Problems

The computational methods that have proven essential for the solution of a large variety of nonlinear elliptic problems are discussed in detail in this book, with particular focus on their application to problems in continuum mechanics and physics. Unlike many books on this topic, the author presents examples of the power and versatility of operator-splitting methods, as well as providing readers with a detailed introduction to alternating direction methods of multipliers and their applicability to the solution of nonlinear (possibly non-smooth) problems from science and engineering. The book also shows how nonlinear least-squares methods, combined with operator-splitting and conjugate gradient algorithms, provide efficient tools for the solution of highly nonlinear problems. Recommended for advanced graduate students and researchers in applied and computational mathematics, as well as research engineers, mathematical physicists, and systems engineers. INDICE: Preface; 1. On some variational problems in Hilbert spaces; 2. Iterative methods in Hilbert spaces; 3. Operator-splitting and alternating direction methods; 4. Augmented Lagrangians and alternating direction methods of multipliers; 5. Least-squares solution of linear and nonlinear problems in Hilbert spaces; 6. Obstacle problems and Bingham flow application to control; 7. – ?2u = ?u3 and other nonlinear eigenvalue problems; 8. Eikonal equations; 9. Fully nonlinear elliptic problems; Epilogue; Bibliography; Index.

• ISBN:
• Editorial: Society for Industrial and Applied Mathematics
• Encuadernacion: Rústica
• Páginas: 445
• Fecha Publicación: 17/12/2015
• Nº Volúmenes: 1
• Idioma: Inglés