Cell-centered and vertex-centered finite volume schemes for the Laplace equationwith homogeneous Dirichlet boundary conditionsare considered on a triangular mesh and on the Voronoi diagram associated to its vertices.A broken P 1 function is constructed from the solutions of both schemes.When the domain is two-dimensional polygonal convex,it is shown that this reconstructionconverges with second-order accuracy towards the exact solution in the L 2 norm,under the sufficient condition that the right-hand side of the Laplace equation belongs to H 1(Ω).
