$(10$ points$)$ Define the element temperature vector as

$d^e=\{d_a^e\}=\{[d_1^e],[d_1^e],[vdots],[d_{n_{en}}^e]{\}}_{n_{en}1}$

where

$d_a^e=u^h(x_a^e)$

Show that the heat flux at any point xin${}^e$ can be calculated from

$q(x)=-D(x)B(x)d^e=-D(x){\displaystyle \underset{a=1}{\overset{n_{en}}{}}}{B}_a{d}_a^e$

where $q(x)$ is the finite element solved for heat flux at the point $x$ that is within the closure of the

element.