Philippe G. Ciarlet
Classics in Applied Mathematics 40
The Finite Element Method for Elliptic Problems is the only book available that analyzes in depth the mathematical foundations of the finite element method. It is a valuable reference and introduction to current research on the numerical analysis of the finite element method, as well as a working textbook for graduate courses in numerical analysis. It includes many useful figures, and there are many exercises of varying difficulty.
Although nearly 25 years have passed since this book was first published, the majority of its content remains up-to-date. Chapters 1 through 6, which cover the basic error estimates for elliptic problems, are still the best available sources for material on this topic. The material covered in Chapters 7 and 8, however, has undergone considerable progress in terms of new applications of the finite element method; therefore, the author provides, in the Preface to the Classics Edition, a bibliography of recent texts that complement the classic material in these chapters.
This book is particularly useful to graduate students, researchers, and engineers using finite element methods. The reader should have knowledge of analysis and functional analysis, particularly Hilbert spaces, Sobolev spaces, and differential calculus in normed vector spaces. Other than these basics, the book is mathematically self-contained.
Preface to the Classics Edition; Preface; General Plan and Interdependence Table; Chapter 1: Elliptic Boundary Value Problems; Chapter 2: Introduction to the Finite Element Method; Chapter 3: Conforming Finite Element Methods for Second Order Problems; Chapter 4: Other Finite Element Methods for Second-Order Problems; Chapter 5: Application of the Finite Element Method to Some Nonlinear Problems; Chapter 6: Finite Element Methods for the Plate Problem; Chapter 7: A Mixed Finite Element Method; Chapter 8: Finite Element Methods for Shells; Epilogue: Some "real-life" finite element model examples; Bibliography; Glossary of Symbols; Index.
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2002 / xxviii + 530 pages / Softcover / ISBN-13: 978-0-898715-14-9 / ISBN-10: 0-89871-514-8 /
List Price $69.50 / SIAM Member Price $48.65 / Order Code CL40