Q$\mathrm{.}2.$ Derive stiffness matrix in the case of Poisson's equation, $-\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{x}}[a\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{x}}]-\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{y}}[a\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{y}}]=f$ for linear four$-$noded rectangular elements. $u(x,y)$ is the field variable $($unknown$).$ HINT: The LHS of the given equation will yield a bilinear symmetric functional, which when used along with substituting the field variable $u=u_j{}_j$ and the weight function $w={}_i,$ will help you to derive the Stiffness matrix.