$-$ Test case $1.$ Fix the left edge completely at the temperature of $0$ and apply a temperature of $100$ to the right edge. Hence, the temperatures of the nodes on the left and right edges are completely prescribed.

$-$ Test case $2.$ Prescribe non$-$homogeneous Dirichlet boundary conditions on all the nodes on the boundary of the body as follows. Prescribe the temperature at each boundary node according to $\backslash ($ T$=100$ X$+100$ Y $\backslash )$ where $"\backslash ($ X $\backslash )"$ and $"\backslash ($ Y $\backslash )"$ correspond to $\backslash ($ X $\backslash )$ and $\backslash ($ Y $\backslash )$ coordinates of each boundary node respectively. For instance the bottom left corner with the coordinates $\backslash ((0,0)\backslash )$ remains completely at the temperature of zero and the top right corner would have the temperature of $200.$