Chapter 10
Hyperbolic Problems
10.1 Conservation Laws
We have successfully applied nite element methods to elliptic and parabolic problems
however, hyperbolic problems will prove to be more di cult. W
Chapter 9
Parabolic Problems
9.1 Introduction
The nite element method may be used to solve time-dependent problems as well as
steady ones. This e ort involves both parabolic and hyperbolic partial di
Chapter 8
Adaptive Finite Element Techniques
8.1 Introduction
The usual nite element analysis would proceed from the selection of a mesh and basis
to the generation of a solution to an accuracy apprai
Chapter 7
Analysis of the Finite Element
Method
7.1 Introduction
Finite element theory is embedded in a very elegant framework that enables accurate a
priori and a posteriori estimates of discretizati
Chapter 6
Numerical Integration
6.1 Introduction
After transformation to a canonical element 0 , typical integrals in the element sti ness
or mass matrices (cf. (5.5.8) have the forms
ZZ
Q=
( )NsNT de
Chapter 5
Mesh Generation and Assembly
5.1 Introduction
There are several reasons for the popularity of nite element methods. Large code segments can be implemented for a wide class of problems. The s
Chapter 4
Finite Element Approximation
4.1 Introduction
Our goal in this chapter is the development of piecewise-polynomial approximations U
of a two- or three-dimensional function u. For this purpose
Chapter 3
Multi-Dimensional Variational
Principles
3.1 Galerkin's Method and Extremal Principles
The construction of Galerkin formulations presented in Chapters 1 and 2 for one-dimensional
problems re
Chapter 2
One-Dimensional Finite Element
Methods
2.1 Introduction
The piecewise-linear Galerkin nite element method of Chapter 1 can be extended in
several directions. The most important of these is m
Chapter 1
Introduction
1.1 Historical Perspective
The nite element method is a computational technique for obtaining approximate solutions to the partial di erential equations that arise in scienti c