This is the only book available that fully analyzes the mathematical foundations of the finite element method. Not only is it valuable reference and introduction to current research, it is also a working textbook for graduate courses in numerical analysis, including useful figures and exercises of varying difficulty.

The objective of this book is to analyze within reasonable limits (it is not a treatise) the basic mathematical aspects of the finite element method. The book should also serve as an introduction to current research on this subject. On the one hand, it is also intended to be a working textbook for advanced courses in Numerical Analysis, as typically taught in graduate courses in American and French universities. For example, it is the author's experience that a one-semester course (on a three-hour per week basis) can be taught from Chapters 1, 2 and 3 (with the exception of Section 3.3), while another one-semester course can be taught from Chapters 4 and 6. On the other hand, it is hoped that this book will prove to be useful for researchers interested in advanced aspects of the numerical analysis of the finite element method. In this respect, Section 3.3, Chapters 5, 7 and 8, and the sections on "Additional Bibliography and Comments should provide many suggestions for conducting seminars.

Research on non-standard finite element methods is evolving rapidly and in this text Brezzi and Fortin give a general framework in which the development is taking place. The presentation is built around a few classic examples: Dirichlet's problem, Stokes problem, Linear elasticity. The authors provide with this publication an analysis of the methods in order to understand their properties as thoroughly as possible.

This book has one single purpose: to present the development of the partial hybrid finite element method for the stress analysis of laminated composite structures. The reason for this presentation is because the authors believe that partial hybrid finite element method is more efficient that the displacement based finite element method for the stress analysis oflaminated composites. In fact, the examples in chapter 5 of this book show that the partial hybrid finite element method is about 5 times more efficient than the displacement based finite element method. Since there is a great need for accurate and efficient calculation of interlaminar stresses for the design using composites, the partial hybrid finite method does provide one possible solution. Hybrid finite method has been in existence since 1964 and a significant amount of work has been done on the topic. However, the authors are not aware of any systematic piece of literature that gives a detailed presentation of the method. Chapters of the displacement finite element method and the evolution 1 and 2 present a sununary of the hybrid finite element method. Hopefully, these two chapters can provide the readers with an appreciation for the difference between the displacement finite element method and the hybrid finite element. It also should prepare the readers for the introduction of partial hybrid finite element method presented in chapter 3.

Non-standard finite element methods, in particular mixed methods, are central to many applications. In this text the authors, Boffi, Brezzi and Fortin present a general framework, starting with a finite dimensional presentation, then moving on to formulation in Hilbert spaces and finally considering approximations, including stabilized methods and eigenvalue problems. This book also provides an introduction to standard finite element approximations, followed by the construction of elements for the approximation of mixed formulations in H(div) and H(curl). The general theory is applied to some classical examples: Dirichlet's problem, Stokes' problem, plate problems, elasticity and electromagnetism.