(untitled) (Journal of Computational Mathematics, 2021)
In this paper the least-squares mixed finite element is considered for solving second-order elliptic problems in two dimensional domains. The primary solution u and the flux σ are approximated using finite element spaces consisting of piecewise polynomials of degree k and r respectively. Based on interpolation operators and an auxiliary projection, superconvergent H^1-error estimates of both the primary solution approximation u_h and the flux approximation σ_h are obtained under the standard quasi-uniform assumption on finite element partition. The superconvergence indicates an accuracy of O(h^r+2) for the least-squares mixed finite element approximation if Raviart-Thomas or Brezzi-Douglas-Fortin-Marini elements of order r are employed with optimal error estimate of O(h^r+1).