Asking abount Finite element interpolation

Question

At first, sorry if my question is a stupid thing. It is about mapping a function into semi-discrete space. Let's see, for the basis function $\{\phi_i(x)\}_{i = 1}^n $, the projection of function $u(x,t)$ in semi-discrete space is $$ u_h(x,t) = \sum_{i = 1}^n u_i(t)\phi_i(x).$$ If we want to construct the projection of $u^2$, we should construct it like this $$ u^2_h(x,t) = \sum_{i = 1}^n u_i^2(t)\phi_i(x)$$ or this: $$ u^2_h(x,t) = \bigg(\sum_{i = 1}^n u_i(t)\phi_i(x)\bigg)^2.$$