I need to integrate an expression like this: $$\int_{S^e} qN_idS$$ where $N_i$ is shape function of isoparameter finite element and $S^e$ is surface facet of domain, for tetrahedron mesh, the surface is triangle. If $q$ is constant within the surface, the above integration can be evulated as follows:$$\int_{S^e} qN_idS=q\frac{area}{3}$$where $area$ is the area of $S^e$.
Now if q is linear within the surface, with known value $q_1$, $q_2$, and $q_3$ at 3 vertices, how to evulate this integration?
Thanks, Tang Laoya
