FINITE ELEMENT ANALYSIS - Joseph E_ Flaherty

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Lecture Notes_ Spring ____

Joseph E_ Flaherty

Amos Eaton Professor

Department of Computer Science

Department of Mathematical Sciences

Rensselaer Polytechnic Institute

Troy_ New York _____

_c _____ Joseph E_ Flaherty_ all rights reserved_ These notes are intended for classroom

use by Rensselaer students taking courses CSCI_ MATH _____ Copying or downloading

by others for personal use is acceptable with noti_cation of the author_

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CSCI_ MATH _____ Finite Element Analysis

Spring ____

Outline

__ Introduction

____ Historical Perspective

____ Weighted Residual Methods

__        _ A Simple Finite Element Problem

__ OneDimensional Finite Element Methods

____ Introduction

____ Galerkin_s Method and Extremal Principles

__        _ Essential and Natural Boundary Conditions

____ Piecewise Lagrange Approximation

___ Hierarchical Bases

____ Interpolation Errors

            _ MultiDimensional 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

___ Threedimensional Bases

____ Interpolation Errors

_ Mesh Generation and Assembly

___ Introduction

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___ Mesh Generation

_          _ Data Structures

___ Coordinate Transformations

__ Generation of Element Matrices and Their Assembly

___ Assembly of Vector Systems

__ Numerical Integration

____ Introduction

____ OneDimensional Gaussian Quadrature

__        _ MultiDimensional Gaussian Quadrature

__ Discretization Errors

____ Introduction

____ Convergence and Optimality

__        _ Perturbations

__ Adaptivity

____ Introduction

____ hRe_nement

__        _ p and hpRe_nement

__ Parabolic Problems

____ Introduction

____ SemiDiscrete Galerkin Methods_ The Method of Lines

__        _ Finite Element Methods in Time

____ Convergence and Stability

___ ConvectionDi_usion Systems

___ Hyperbolic Problems

_____ Introduction

_____ Flow Problems and Upwind Weighting

___      _ Arti_cial Di_usion

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_____ Streamline Weighting

___ Linear Systems Solution

_____ Introduction

_____ Banded Gaussian Elimination and Pro_le Techniques

___      _ Nested Dissection and Domain Decomposition

_____ Conjugate Gradient Methods

____ Nonlinear Problems and Newton_s Method

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