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We study the Oliker-Prussner method exploiting its geometric nature. Wederive discrete stability and continuous dependence estimates in the max-normby using a discrete Alexandroff estimate and the Brunn-Minkowski inequality. Weshow that the method is exact for all convex quadratic polynomials provided theunderlying set of nodes is translation invariant within the domain; nodes stillconform to the domain boundary. This gives a suitable notion of operatorconsistency which, combined with stability, leads to pointwise rates ofconvergence for classical and non-classical solutions of the Monge-Amp\`{e}reequation.

Pointwise rates of convergence for the Oliker-Prussner method for the Monge-Amp\`{e}re equation