2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/186309Centered finite volume methods are considered in the context of Numerical Relativity. A specific formulation is presented, in which third-order space accuracy is reached by using a piecewise-linear reconstruction. This formulation can be interpreted as an 'adaptive viscosity' modification of centered finite difference algorithms. These points are fully confirmed by 1D black-hole simulations. In the 3D case, evidence is found that the use of a conformal decomposition is a key ingredient for the robustness of black hole numerical codes.Revised version, 10 pages, 6 figures. To appear in Phys. Rev. DGeneral Relativity and Quantum Cosmologytext