  In this note we study the convergence of monotone P1 finite element methods
on unstructured meshes for fully non-linear Hamilton-Jacobi-Bellman equations
arising from stochastic optimal control problems with possibly degenerate,
isotropic diffusions. Using elliptic projection operators we treat
discretisations which violate the consistency conditions of the framework by
Barles and Souganidis. We obtain strong uniform convergence of the numerical
solutions and, under non-degeneracy assumptions, strong L2 convergence of the
gradients.
