Superconvergence error estimates for the div least-squares finite element method on elliptic problems

In this paper we discuss the error estimations for the div least-squares finite element method on elliptic problems. Compared with the previous work, we present a complete error analysis, which improves the current state-of-the-art results. The error estimations for both the scalar and the flux variables are established by dual arguments, and in most cases, only an H^1+ε regularity is used. Numerical experiments strongly confirm our analysis.