Finite Element Solution Of Boundary Value Problems: Theory And Computation (computer Science & Applied Mathematics)

Finite Element Solution of Boundary Value Problems: Theory and Computation provides a thorough, balanced introduction to both the theoretical and the computational aspects of the finite element method for solving boundary value problems for partial differential equations. Although significant advances have been made in the finite element method since this book first appeared in 1984, the basics have remained the same, and this classic, well-written text explains these basics and prepares the reader for more advanced study. Useful as both a reference and a textbook, complete with examples and exercises, it remains as relevant today as it was when originally published Finite Element Solution of Boundary Value Problems: Theory and Computation provides an introduction to both the theoretical and computational aspects of the finite element method for solving boundary value problems for partial differential equations. This book is composed of seven chapters and begins with surveys of the two kinds of preconditioning techniques, one based on the symmetric successive overrelaxation iterative method for solving a system of equations and a form of incomplete factorization. The subsequent chapters deal with the concepts from functional analysis of boundary value problems. These topics are followed by discussions of the Ritz method, which minimizes the quadratic functional associated with a given boundary value problem over some finite-dimensional subspace of the original space of functions. Other chapters are devoted to direct methods, including Gaussian elimination and related methods, for solving a system of linear algebraic equations. The final chapter continues the analysis of preconditioned conjugate gradient methods, concentrating on applications to finite element problems. This chapter also looks into the techniques for reducing rounding errors in the iterative solution of finite element equations. This book will be of value to advanced undergraduates and graduates in the areas of numerical analysis, mathematics, and computer science, as well as for theoretically inclined workers in engineering and the physical sciences. Content: Front Matter, Page iii Copyright, Page iv Dedication, Page v Preface, Pages ix-xii Acknowledgments, Pages xiii-xiv List of Symbols, Pages xv-xviii CHAPTER 1 - Quadratic Functionals on Finite-Dimensional Vector Spaces, Pages 1-63 CHAPTER 2 - Variational Formulation of Boundary Value Problems: Part I, Pages 64-100 CHAPTER 3 - Variational Formulation of Boundary Value Problems: Part II, Pages 101-144 CHAPTER 4 - The Ritz–Galerkin Method, Pages 145-162 CHAPTER 5 - The Finite Element Method, Pages 163-267 CHAPTER 6 - Direct Methods for Solving Finite Element Equations, Pages 268-326 CHAPTER 7 - Iterative Solution of Finite Element Equations, Pages 327-421 APPENDIX A - Chebyshev Polynomials, Pages 422-425 Index, Pages 427-432 Computer Science and Applied Mathematics: A SERIES OF MONOGRAPHS AND TEXTBOOKS, Pages ibc1-ibc2