Following figure shows an element on the face of a thin rectangular plate of thickness $z.$ The plate is insulated everywhere but at its edges, where the temperature can be set at a prescribed level. The insulation and the thinness of the plate mean that heat transfer is limited to the $x$ and $y$ dimensions. At steady state, the flow of heat into the element over a unit time period $t$ must equal the flow out. Energy balance on this plate results in Laplace equation:

$\frac{de{l}^{2}T}{del{x}^2}+\frac{de{l}^{2}T}{del{y}^2}=0$

Use Gauss$-$Seidel to solve for the temperature of defined four points on the heated plate with an intervals of $x=y.$