Understanding and Implementing the Finite Element Method / Edition 1

by Mark S. Gockenbach

Overview

The finite element method is the most powerful general-purpose technique for computing accurate solutions to partial differential equations. This book contains a thorough derivation of the finite element equations as well as sections on programming the necessary calculations, solving the finite element equations, and using a posteriori error estimates to produce validated solutions. Accessible introductions to advanced topics, such as multigrid solvers, the hierarchical basis conjugate gradient method, and adaptive mesh generation, are provided. Each chapter ends with exercises to help readers master these topics. The book is practical in nature. It includes a carefully documented collection of MATLAB programs implementing the ideas presented. Readers will benefit from a detailed explanation of data structures and specific coding strategies and will learn how to write a finite element code from scratch. Students can use the MATLAB codes to experiment with the method and extend them in various ways.

Product Details

ISBN-13:	9780898716146
Publisher:	SIAM
Publication date:	11/28/2006
Edition description:	New Edition
Pages:	392
Product dimensions:	67.50(w) x 97.50(h) x 7.50(d)

About the Author

Mark S. Gockenbach is a Professor of Mathematical Sciences at Michigan Technological University. His research interests include inverse problems, computational optimization, and mathematical software. His first book, Partial Differential Equations: Analytical and Numerical Methods, was published by SIAM in 2002.

Table of Contents

Preface; Part I. The Basic Framework for Stationary Problems: 1. Some model PDEs; 2. The weak form of a BVP; 3. The Galerkin method; 4. Piecewise polynomials and the finite element method; 5. Convergence of the finite element method; Part II. Data Structures and Implementation: 6. The mesh data structure; 7. Programming the finite element method: Linear Lagrange triangles; 8. Lagrange triangles of arbitrary degree; 9. The finite element method for general BVPs; Part III. Solving the Finite Element Equations: 10. Direct solution of sparse linear systems; 11. Iterative methods: Conjugate gradients; 12. The classical stationary iterations; 13. The multigrid method; Part IV. Adaptive Methods: 14. Adaptive mesh generation; 15. Error estimators and indicators; Bibliography; Index.

Editorial Reviews

'Upon completion of this book a student or researcher would be well prepared to employ finite elements for an application problem or proceed to the cutting edge of research in finite element methods. The accuracy and the thoroughness of the book are excellent.' Anthony Kearsley, National Institute of Standards and Technology

From the Publisher