TY - JOUR
T1 - Superconvergence of Least-Squares Mixed Finite Element for Second-Order Elliptic Problems
AU - Chen , Yan-Ping
AU - Yu , De-Hao
JO - Journal of Computational Mathematics
VL - 6
SP - 825
EP - 832
PY - 2003
DA - 2003/12
SN - 21
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/10238.html
KW - Elliptic problem, Superconvergence, Interpolation projection, Least-squares mixed finite element.
AB - <p style="text-align: justify;">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 $\sigma$ 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 $\sigma_h$ 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 $O(h^{r+1})$.</p>