Numerical Methods for Nonlinear Partial Differential Equations

1. Introduction.- Part I: Analytical and Numerical Foundations.- 2. Analytical Background.- 3. FEM for Linear Problems.- 4. Concepts for Discretized Problems.- Part II: Approximation of Classical Formulations.- 5. The Obstacle Problem.- 6. The Allen-Cahn Equation.- 7. Harmonic Maps.- 8. Bending Problems.- Part III: Methods for Extended Formulations.- 9. Nonconvexity and Microstructure.- 10. Free Discontinuities.- 11. Elastoplasticity.- Auxiliary Routines.- Frequently Used Notation.- Index.

"This book presents an ambitious overview of modern results and trends in the field of numerical methods for nonlinear PDEs, with an emphasis on the finite element method. ... The target audience of the book is postgraduates and experienced researchers. ... this is an excellent monograph describing methods found at the intersection of numerical PDEs and the calculus of variations." (Michael Neilan, SIAM Review, Vol. 58 (3), September, 2016)

"This book provides advanced students and experimental researchers with an introduction to numerical methods for nonlinear partial differential equations, in particular those originating from continuum mechanics. ... This book presents a very nice transition from graduate-level material to state-of-the-art research topics. ... This is a nice and well-written advanced textbook." (Karsten Urban, Mathematical Reviews, October, 2015)