We construct an algorithm for estimating the capacity of nice compact subsets of the plane. Our method is based on a relation between capacity and Green's function together with a uniform harmonic approximation theorem. We use the simple least-square technique and, what is most important, we can obtain a bound on the error made in the estimated capacity.
"Computing logarithmic capacity with linear programming." Experiment. Math. 6 (3) 221 - 238, 1997.