Superconvergence of Least-Squares Mixed Finite Element for Second-Order Elliptic Problems

Superconvergence of Least-Squares Mixed Finite Element for Second-Order Elliptic Problems

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.

Author Details

Yan-Ping Chen

De-Hao Yu