$(25$ points$)$ Matlab Code needed

Repeat book problem $4\mathrm{.}4$ d using a $3$ noded element where the trial and weight

function approximations are given by the incomplete polynomial $($but with a

linear complete approximation$)$:

${}^e={}_0^e+{}_1^{e}x+{}_2^e{x}^4$

Compare the results to the linear approximation.

Part $4$ d $.$ referenced in question $3$ is below

d$.$ The error of an interpolation is generally measured by what is called a $L_2$ norm. The error in the $L_2$ norm,

which we denote by e$,$ is given by

$e^2={\displaystyle \underset{0}{\overset{L}{}}}(u^e-u{)}^{2}dx$

where $u(x)=x^3$ in this case. Compute the error e for meshes of two, four and eight linear displacement

elements. Use Gauss quadrature for integration. Then plot $($this can be done manually$)$ the error versus

the element size on a log$-$log plot. This should almost be a straight line. What is its slope? This slope is

indicative of the rate of convergence of the element.