A least-squares Galerkin approach to gradient and Hessian recovery for nondivergence-form elliptic equations

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