@Article{JCM-21-6,
author = {Yan-Ping, Chen and Yu, De-Hao},
title = {Superconvergence of Least-Squares Mixed Finite Element for Second-Order Elliptic Problems},
journal = {Journal of Computational Mathematics},
year = {2003},
volume = {21},
number = {6},
pages = {825--832},
abstract = {<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>},
issn = {1991-7139},
doi = {https://doi.org/2003-JCM-10238},
url = {https://global-sci.com/article/85380/superconvergence-of-least-squares-mixed-finite-element-for-second-order-elliptic-problems}
}