كتاب Finite Element Analysis

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Finite Element Analysis
Joseph E. Flaherty
Amos Eaton Professor

ويتناول الموضوعات الأتية :

Outline
Introduction
Historical Perspective
Weighted Residual Methods
A Simple Finite Element Problem
One
Dimensional Finite Element Methods
Introduction
Galerkin's Method and Extremal Principles
Essential and Natural Boundary Conditions
Piecewise Lagrange Approximation

Hierarchical Bases
Interpolation Errors
Multi
Dimensional Variational Principles
Galerkin's Method and Extremal Principles
Function Spaces and Approximation
Overview of the Finite Element Method
Finite Element Approximation
Introduction
Lagrange Bases on Triangles
Lagrange Bases on Rectangles
Hierarchical Bases

Three
dimensional Bases
Interpolation Errors

Mesh Generation and Assembly

Introduction
iii
Mesh Generation

Data Structures

Coordinate Transformations

Generation of Element Matrices and Their Assembly

Assembly of Vector Systems
Numerical Integration
Introduction
One
Dimensional Gaussian Quadrature
Multi
Dimensional Gaussian Quadrature
Discretization Errors
Introduction
Convergence and Optimality
Perturbations
Adaptivity
Introduction
h
Refnement
p
and hp
Refnement
Parabolic Problems
Introduction
Semi
Discrete Galerkin Methods The Method of Lines
Finite Element Methods in Time
Convergence and Stability

Convection
Diusion Systems
Hyperbolic Problems
Introduction
Flow Problems and Upwind Weighting
Artifcial Diffusion
iv Streamline Weighting
Linear Systems Solution
Introduction
Banded Gaussian Elimination and Profle Techniques
Nested Dissection and Domain Decomposition
Conjugate Gradient Methods
Nonlinear Problems and Newton's Method

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