The stabilized least-squares nonconforming mixed finite element approximation for the convection-diffusion problem

In this paper, we use a nonconforming mixed finite element to approximate the convection-diffusion problem by the stabilized least-squares method. we convert the original system of second-order partial differential equations into a first-order system formulation by a additional variable. The existence and uniqueness of the approximate solutions are proved. The convergence analysis is presented and the optimal error estimates for the stress in H(div)-norm and the displacement in broken H¹-norm are derived.