Finite element solution of boundary value problems : theory and computation /
Finite Element Solution of Boundary Value Problems.
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| Format: | eBook |
| Language: | English |
| Language Notes: | English. |
| Published: |
Orlando, Fla. :
Academic Press,
1984.
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| Series: | Computer science and applied mathematics.
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| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Front Cover; Finite Element Solution of Boundary Value Problems: Theory and Computation; Copyright Page; Dedication; Table of Contents; Preface; Acknowledgments; List of Symbols; CHAPTER 1. Quadratic Functionals on Finite-Dimensional Vector Spaces; Introduction; 1.1 Quadratic Functionals; 1.2 The Method of Steepest Descent; 1.3 The Conjugate Gradient Method; 1.4 The Preconditioned Conjugate Gradient Method; Exercises; References; CHAPTER 2. Variational Formulation of Boundary Value Problems: Part I; Introduction; 2.1 The Euler-Lagrange Equation for One-Dimensional Problems
- 2.2 Natural and Essential Boundary Conditions2.3 Problems in Two and Three Dimensions; 2.4 Boundary Value Problemsin Physics and Engineering; Exercises; References; CHAPTER 3. Variational Formulation of Boundary Value Problems: Part II; Introduction; 3.1 The Concept of Completion; 3.2 The Lax-Milgram Lemma and Applications; 3.3 Regularity, Symbolic Functions, and Green's Functions; Exercises; References; CHAPTER 4. The Ritz-Galerkin Method; Introduction; 4.1 The Ritz Method; 4.2 Error Analysis of the Ritz Method; 4.3 The Galerkin Method
- 4.4 Application of the Galerkin Method to Noncoercive ProblemsExercises; References; CHAPTER 5. The Finite Element Method; Introduction; 5.1 Finite Element Basis Functions; 5.2 Assembly of the Ritz-Galerkin System; 5.3 Isoparametric Basis Functions; 5.4 Error Analysis; 5.5 Condition Numbers; 5.6 Singularities; Exercises; References; CHAPTER 6. Direct Methods for Solving Finite Element Equations; Introduction; 6.1 Band Matrices; 6.2 Direct Methods; 6.3 Special Techniques; 6.4 Error Analysis; Exercises; References; CHAPTER 7. Iterative Solution of Finite Element Equations; Introduction
- 7.1 SSOR Preconditioning7.2 Preconditioning by Modified Incomplete Factorization : Part I; 7.3 Preconditioning by Modified Incomplete Factorization : Part II; 7.4 Calculation of Residuals: Computational Labor and Stability; 7.5 Comparison of Iterative and Direct Methods; 7.6 Multigrid Methods; Exercises; References; APPENDIX A: Chebyshev Polynomials; Index