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.

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Yes, you can access Finite Element Solution of Boundary Value Problems by O. Axelsson,V. A. Barker, Werner Rheinboldt in PDF and/or ePUB format, as well as other popular books in Mathematics & Calculus. We have over one million books available in our catalogue for you to explore.

Information

Publisher

Academic Press

Year

2014

ISBN

9781483260563

Topic

Mathematics

Subtopic

Calculus

Index

Mathematics

Front Cover
Finite Element Solution of Boundary Value Problems: Theory and Computation
Copyright Page
Table of Contents
Dedication
Preface
Acknowledgments
List of Symbols
CHAPTER 1. Quadratic Functionals on Finite-Dimensional Vector Spaces
CHAPTER 2. Variational Formulation of Boundary Value Problems: Part I
CHAPTER 3. Variational Formulation of Boundary Value Problems: Part II
CHAPTER 4. The Ritz–Galerkin Method
CHAPTER 5. The Finite Element Method
CHAPTER 6. Direct Methods for Solving Finite Element Equations
CHAPTER 7. Iterative Solution of Finite Element Equations
APPENDIX A: Chebyshev Polynomials
Index