Consider simultaneous steady$-$state conduction and radiation in a plate. The mathematical model of this problem is given by

$\frac{d}{dx}(k()\frac{d}{dx})=0,0x1$

$(0)=0,(1)=1$

where $k$ is the thermal conductivity given by

$k()=1+\frac{3}{4}$

Develop the weak form and a finite element model for this problem using four linear elements. Solve this problem using the method of successive substitution, using the initial value $=\frac{1}{2}$ for $0.$ Perform four iterations.