We present a technique for the approximation of quadratic
variational problems of the first order in spaces of piece-wise
constant functions. The method adopts ideas from the theory of
$\Gamma$-convergence as a guideline, and it differs from more
traditional non-conforming techniques because it is based on the
introduction of a suitable sequence of discrete functionals to be
minimized with no constraints and without requiring that the
spline functions fulfill any patch test condition.
