  We propose an arbitrary-order discontinuous Galerkin method for second-order
elliptic problem on general polygonal mesh with only one degree of freedom per
element. This is achieved by locally solving a discrete least-squares over a
neighboring element patch. Under a geometrical condition on the element patch,
we prove an optimal a priori error estimates for the energy norm and for the
L$^2$ norm. The accuracy and the efficiency of the method up to order six on
several polygonal meshes are illustrated by a set of benchmark problems.
