  In this paper, we present a novel penalty approach for the numerical solution
of continuously controlled HJB equations and HJB obstacle problems. Our results
include estimates of the penalisation error for a class of penalty terms, and
we show that variations of Newton's method can be used to obtain globally
convergent iterative solvers for the penalised equations. Furthermore, we
discuss under what conditions local quadratic convergence of the iterative
solvers can be expected. We include numerical results demonstrating the
competitiveness of our methods.
