  Recently, Krylov, Barles, and Jakobsen developed the theory for estimating
errors of monotone approximation schemes for the Bellman equation (a convex
Isaacs equation). In this paper we consider an extension of this theory to a
class of non-convex multidimensional Isaacs equations. This is the first result
of this kind for non-convex multidimensional fully non-linear problems.
  To get the error bound, a key intermediate step is to introduce a
penalization approximation. We conclude by (i) providing new error bounds for
penalization approximations extending earlier results by e.g. Benssousan and
Lions, and (ii) obtaining error bounds for approximation schemes for the
penalization equation using very precise a priori bounds and a slight
generalization of the recent theory of Krylov, Barles, and Jakobsen.
