The Mathematics of Finite Elements and Applications - 1st Edition - ISBN: 9780127472508, 9781483268842

The Mathematics of Finite Elements and Applications

1st Edition

Proceedings of the Brunel University Conference of the Institute of Mathematics and Its Applications Held in April 1972

Editors: J. R. Whiteman
eBook ISBN: 9781483268842
Imprint: Academic Press
Published Date: 28th January 1973
Page Count: 534
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The Mathematics of Finite Elements and Applications provides information pertinent to the mathematics of finite elements, applications, algorithms, and computational techniques. This book discusses the developments in the mathematics of finite elements.

Organized into 32 chapters, this book begins with an overview of the basis of the finite element process as a general approximation tool. This text then examines the methods for obtaining bounds on the errors in finite element solutions to two-dimensional elliptic boundary value problems defined on simply connected polygonal regions. Other chapters consider the practical implementation of the Galerkin and the Rayleigh–Ritz methods to equations of importance to physics and engineering. This book discusses as well a fundamental investigation into the problem of convergence in the finite element method. The final chapter deals with an algorithm that is applicable to the analysis of arbitrary plane stress or plane strain configurations.

This book is a valuable resource for numerical analysts, mathematical physicist, applied mathematicians, computer scientists, and engineers.

Table of Contents



Finite Elements-The Background Story

An Introduction to the Mathematics of the Finite Element Method

Some Recent Advances in the Mathematics of Finite Elements

Error Analysis of Finite Element Methods With Triangles for Elliptic Boundary Value Problems

Orders of Convergence in Finite Element Methods

Finite Elements with Harmonic Interpolation Functions

Variational Finite Element Methods for Initial Value Problems

A Least Squares Finite Element Solution of Nonlinear Operators

The l2 and l∞ Condition Numbers of the Finite Element Stiffness and Mass Matrices, and the Pointwise Convergence of the Method

Dual Formulations for Potential and Complementary Energies. Unilateral Boundary Conditions. Applications to the Finite Element Method

Generalised Matrix Inverse Techniques for Local Approximations of Operator Equations

Finite Element Solution of Unsteady and Unsaturated Flow in Porous Media

Sufficient Conditions for Convergence in the Finite Element Method for Any Solution of Finite Energy

Combined Application of Finite Element Methods and Richardson Extrapolation to the Torsion Problem

Finite Element Applications in Mathematical Physics

A Dynamic Elastoplastic Analysis of Thin Shells of Revolution Under Asymmetric Mechanical and Thermal Loading

On Hybrid Finite Elements

Some Free Surface Transient Flow Problems of Seepage and Irrotational Flow

Calculation of Stress Intensity Factors at Crack Tips Using Special Finite Elements

Singularities in Transmission Lines

Application of the Finite Element Method to the Extensional Vibrations of Piezoelectric Plates

Vibration of Curved Structures Using Quadrilateral Finite Elements

Assessment of Accuracies of Finite Element Eigenvalues

Flexibility and Stiffness Matrices for an Open-Tube Warping Constraint Finite Element

A Sandwich Plate Finite Element

Application of Three-Dimensional Finite Elements for Analysis of Irradiation-Induced Stresses in Nuclear Reactor Fuel Elements

The Analysis and Application of Sparse Matrix Algorithms in the Finite Element Method

The Comparison of Iterative and Direct Solution Techniques in the Analysis of Time-Dependent Stress Problems, Including Creep

A Method for Simulating Concentrated Forces and Local Reinforcements in Stress Computation

Some Practical Solution Techniques for Finite Element Analysis

Algorithm for the Large Deflection Geometrically Nonlinear Plane and Curved Structures

Automated Solutions of Time Dependent Problems


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© Academic Press 1973
Academic Press
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About the Editor

J. R. Whiteman

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