A Sequential Least Squares Method for Elliptic Equations in Non-Divergence Form

We develop a new least squares method for solving the second-order elliptic equations in non-divergence form. Two least-squares-type functionals are proposed two steps. first obtain numerical approximation to gradient piecewisely irrotational polynomial space. Then together with gradient, we seek solution of primitive variable continuous finite element The variational setting naturally provides posteriori error which could be used an adaptive refinement algorithm. estimates $L^2$ norm and energy norms both unknowns derived. By series experiments, verify convergence rates show efficiency