Study guide: Introduction to finite element methods

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Example: linear approximation; problem

Problem.

Approximate a parabola $f(x) = 10(x-1)^2 - 1$ by a straight line.

$\begin{equation*} V = \hbox{span}\,\{1, x\} \end{equation*}$ That is,

$\baspsi_0(x)=1$ ,

$\baspsi_1(x)=x$ , and

$N=1$ . We seek

$\begin{equation*} u=c_0\baspsi_0(x) + c_1\baspsi_1(x) = c_0 + c_1x \end{equation*}$