Unformatted text preview: ese are being used to verify the accuracy of the
computation, and also to control an adaptive process whereby meshes are automatically
re ned and coarsened and/or the degrees of polynomial approximations are varied so as
to compute solutions to desired accuracies in an optimal fashion 1, 2, 3, 4, 5, 7, 14]. 1.2 Weighted Residual Methods
Our goal, in this introductory chapter, is to introduce the basic principles and tools of
the nite element method using a linear two-point boundary value problem of the form
L u] := ; d (p(x) du ) + q(x)u = f (x)
u(0) = u(1) = 0: 0<x<1 (1.2.1a)
(1.2.1b) The nite element method is primarily used to address partial di erential equations and is
hardly used for two-point boundary value problems. By focusing on this problem, we hope
to introduce the fundamental concepts without the geometric complexities encountered
in two and three dimensions.
Problems like (1.2.1) arise in many situations including the longitudinal deformation
of an elastic rod, steady heat conduction, and the transverse de ection of a supported 1.2....
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