The purpose of this primer is to provide the basics of the Finite Element Method primarily
illustrated through a classical model problem linearized elasticity. The topics covered are: -
Weighted residual methods and Galerkin approximations - A model problem for one-dimensional
linear elastostatics - Weak formulations in one dimension - Minimum principles in one
dimension - Error estimation in one dimension - Construction of Finite Element basis functions
in one dimension - Gaussian Quadrature - Iterative solvers and element by element data
structures - A model problem for three-dimensional linear elastostatics - Weak formulations
in three dimensions - Basic rules for element construction in three-dimensions - Assembly of
the system and solution schemes - An introduction to time-dependent problems and - An
introduction to rapid computation based on domain decomposition and basic parallel processing.
The approach is to introduce the basic concepts first in one-dimension then move on to
three-dimensions. A relatively informal style is adopted. This primer is intended to be a
starting point which can be later augmented by the large array of rigorous detailed books in
the area of Finite Element analysis. In addition to overall improvements to the first edition
this second edition also adds several carefully selected in-class exam problems from exams
given over the last 15 years at UC Berkeley as well as a large number of take-home computer
projects. These problems and projects are designed to be aligned to the theory provided in the
main text of this primer.
