The finite element method : an introduction with partial differential equations / A.J. Davies.

CONTENT

1 Historical introduction

2 Weighted residual and variational methods
2.1 Classification of differential operators
2.2 Self-adjoint positive definite operators
2.3 Weighted residual methods
2.4 Extremum formulation: homogeneous boundary conditions
2.5 Non-homogeneous boundary conditions
etc.

3 The finite element method for elliptic problems
3.1 Difficulties associated with the application of weighted residual methods
3.2 Piecewise application of the Galerkin method
3.3 Teminology
3.4 Finite element idealization
3.5 Illustrative problem involving one independent variable
etc.

4 Higher order elements: the isoparametric concept
4.1 A two point boundary value problem
4.2 Higher order rectangular elements
4.3 Higher order triangular elements
4.4 Two degrees of freedom at each node
4.5 Condensation of internal nodal freedoms
etc.

5 Further topics in the finite element method
5.1 The variational approach
5.2 Collocation and least squares method
5.3 use of Galerkin's method for time dependent and non linear problems
5.4 Time dependent problems using variational principles which are not extremal
5.5 The Laplace transform
etc.

6 Convergence of the finite element method
6.1 A one dimensional example
6.2 Two dimensional problems involving Poisson's equation
6.3 Isoparametric elements: numerical integration
6.4 Non conforming elements: the patch test
6.5 Comparison with the finite difference method: stability
etc.

7 The boundary element method
7.1 Integral formulation of boundary value problems
7.2 boundary element idealization for Laplace's equation
7.3 A constant boundary element for Laplace's equation
7.4 A linear element for Laplace's equation
7.5 Time dependent problems
etc.

8 Computational aspects
8.1 Pre-processor
8.2 Solution phase
8.3 Post processor
8.4 Finite element method or boundary element method

References :p. 288 - 294 ._ Index : p. 295 - 297