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A Finite Element Primer for Beginners - The Basics (Paperback, 2nd ed. 2018)
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A Finite Element Primer for Beginners - The Basics (Paperback, 2nd ed. 2018)
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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.
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