In the finite element lecture we learned, that it is impractical to use centre of gravity of a triangle as a degree of freedom. So we defined a subspace $P_3'$, where $P_2\subseteq P_3'\subseteq P_3$$$P_3'=\{p\in P_3;\ p(a_{123})=-\frac{1}{6}\sum_{l=1,2,3}p(a_l)+\frac{1}{4}\sum_{l,m=1,2,3,\ l\neq m}p(a_{llm})\}$$where $a_1$, $a_2$, $a_3$ form a triangle in 2 dimensions, $a_{llm}=\frac{1}{3}(2a_l+a_m)$.What is the reason for this? Why don't we use the centre of gravity?
Why do we eliminate centre of gravity as degree of freedom in FEM
finite element