  The elliptic 2-Hessian equation is a fully nonlinear partial differential
equation (PDE) that is related to intrinsic curvature for three dimensional
manifolds. We introduce two numerical methods for this PDE: the first is
provably convergent to the viscosity solution, and the second is more accurate,
and convergent in practice but lacks a proof. The PDE is elliptic on a
restricted set of functions: a convexity type constraint is needed for the
ellipticity of the PDE operator. Solutions with both discretizations are
obtained using Newton's method. Computational results are presented on a number
of exact solutions which range in regularity from smooth to nondifferentiable
and in shape from convex to non convex.
