Least-Squares Finite Element Methods

Survey of Variational Principles and Associated Finite Element Methods..- Classical Variational Methods.- Alternative Variational Formulations.- Abstract Theory of Least-Squares Finite Element Methods.- Mathematical Foundations of Least-Squares Finite Element Methods.- The Agmon#x2013;Douglis#x2013;Nirenberg Setting for Least-Squares Finite Element Methods.- Least-Squares Finite Element Methods for Elliptic Problems.- Scalar Elliptic Equations.- Vector Elliptic Equations.- The Stokes Equations.- Least-Squares Finite Element Methods for Other Settings.- The Navier#x2013;Stokes Equations.- Parabolic Partial Differential Equations.- Hyperbolic Partial Differential Equations.- Control and Optimization Problems.- Variations on Least-Squares Finite Element Methods.- Supplementary Material.- Analysis Tools.- Compatible Finite Element Spaces.- Linear Operator Equations in Hilbert Spaces.- The Agmon#x2013;Douglis#x2013;Nirenberg Theory and Verifying its Assumptions.

From the reviews:

“In the book under review, the authors give a unified and comprehensive treatment of least-squares finite element methods and discuss important implementation issues that are critical to their success in practice. … This book is valuable both for researchers and practitioners working in least-squares finite element methods. … In addition, others will find it a great reference for learning about the theory and implementation of the least-squares finite element methods.” (Tsu-Fen Chen, Mathematical Reviews, Issue 2010 b)