Least-Squares Streamline Diffusion Finite Element Approximations To Singularly Perturbed Convection-Diffusion Problems

In this paper we introduce and study a least-squares finite element approximation for singularly perturbed convection-diffusion equations of second order. By introducing the flux (diffusive plus convective) as a new unknow the problem is written in a mixed form as a first order system. Further, the flux is augmented by adding the lower order terms with a small parameter. The new first order system is approximated by the least-squares finite element method using the minus one norm approach of Bramble, Lazarov, and Pasciak [2]. Further, we estimate the error of the method and discuss its implementation and the numerical solution of some test problems.