Problem $5\mathrm{.}1$

Consider a heat conduction problem in the domain $[0,20]m.$ The bar has a unit cross section, constant

thermal conductivity $k=5W{C}^{-1}{m}^{-1}$ and a uniform heat source $s=100W{m}^{-1}.$ The boundary

conditions are $)=(0$ and $)=(20.$ Solve the problem with two equal linear

elements. Plot the finite element solution $T^h(x)$ and $d{T}^h\frac{x}{d}x$ and compare to the exact solution which is

given by $T(x)=-10x^2+400x.$

For book problem $5\mathrm{.}1$ do it by hand first and then write a code to do it$.$ The code should

have functions$/$subroutines to

compute the element shape functions and $B$ matrix

compute element stiffness and loads

assemble the element matrices $($it is fine to use the $"$L$"$ matrices to do the assembly$)$ into

the global matrices