  This paper is concerned with the convergence rate of policy iteration for
(deterministic) optimal control problems in continuous time. To overcome the
problem of ill-posedness due to lack of regularity, we consider a semi-discrete
scheme by adding a viscosity term via finite differences in space. We prove
that PI for the semi-discrete scheme converges exponentially fast, and provide
a bound on the error induced by the semi-discrete scheme. We also consider the
discrete space-time scheme, where both space and time are discretized.
Convergence rate of PI and the discretization error are studied.
