How to define $P0-$ Piecewise constant basis function in finite element method?

Suppose if we take $$X_h(G)$$ as finite element space then this space (space of piecewise constant basis function)is defined as

$$X_h=\{v: v|_{T}=c_{T}, T \in \mathbb{T}\},$$ where $$\mathbb{T}$$ is a subdivision of domain $$G$$. Then my main question is

"How to define (or fix value) of constant $$c_T$$"?

• I'm not sure if I understand your question. The $c_T$'s are your unknown degrees-of-freedom. They are free to vary -- that's what makes $X_h$ a space, not just a function. A member of that space, say $u \in X_h$, would correspond to defining the values of the $c_T$'s. – LedHead Aug 23 '19 at 17:49