Year: 2003
Author: Yan-Ping Chen, De-Hao Yu
Journal of Computational Mathematics, Vol. 21 (2003), Iss. 6 : pp. 825–832
Abstract
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 $O(h^{r+1})$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2003-JCM-10238
Journal of Computational Mathematics, Vol. 21 (2003), Iss. 6 : pp. 825–832
Published online: 2003-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 8
Keywords: Elliptic problem Superconvergence Interpolation projection Least-squares mixed finite element.