Volume 21, Issue 6
Superconvergence of Least-Squares Mixed Finite Element for Second-Order Elliptic Problems

Yan-ping Chen & De-hao Yu

DOI:

J. Comp. Math., 21 (2003), pp. 825-832

Published online: 2003-12

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  • 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 $O(h^{r+1})$.

  • Keywords

Elliptic problem Superconvergence Interpolation projection Least-squares mixed finite element

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@Article{JCM-21-825, author = {Yan-ping Chen and De-hao Yu}, 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 = { 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 $O(h^{r+1})$. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10238.html} }
TY - JOUR T1 - Superconvergence of Least-Squares Mixed Finite Element for Second-Order Elliptic Problems AU - Yan-ping Chen & De-hao Yu 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 KW - Superconvergence KW - Interpolation projection KW - Least-squares mixed finite element AB - 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 $O(h^{r+1})$.
Yan-ping Chen & De-hao Yu. (1970). Superconvergence of Least-Squares Mixed Finite Element for Second-Order Elliptic Problems. Journal of Computational Mathematics. 21 (6). 825-832. doi:
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