  We propose a least-squares method involving the recovery of the gradient and
possibly the Hessian for elliptic equation in nondivergence form. As our
approach is based on the Lax--Milgram theorem with the curl-free constraint
built into the target (or cost) functional, the discrete spaces require no
inf-sup stabilization. We show that standard conforming finite elements can be
used yielding apriori and aposteriori convergnece results. We illustrate our
findings with numerical experiments with uniform or adaptive mesh refinement.
