  In this short note we investigate the numerical performance of the method of
artificial diffusion for second-order fully nonlinear Hamilton-Jacobi-Bellman
equations. The method was proposed in (M. Jensen and I. Smears,
arxiv:1111.5423); where a framework of finite element methods for
Hamilton-Jacobi-Bellman equations was studied theoretically. The numerical
examples in this note study how the artificial diffusion is activated in
regions of degeneracy, the effect of a locally selected diffusion parameter on
the observed numerical dissipation and the solution of second-order fully
nonlinear equations on irregular geometries.
