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1999•SIAM Journal on Numerical AnalysisRequires access

Superconvergence of Mixed Finite Element Approximations over Quadrilaterals

Richard E. Ewing, Michael M. Liu, Junping Wang

Open publisher page 84 citations

Abstract

A superconvergence result is established in this article for approximate solutions of second-order elliptic equations by mixed finite element methods over quadrilaterals. The superconvergence indicates an accuracy of ${\cal O}(h^{k+2})$ for the mixed finite element approximation if the Raviart--Thomas or Brezzi--Douglas--Fortin--Marini elements of order k are employed with optimal error estimate of ${\cal O}(h^{k+1})$. Numerical experiments are presented to illustrate the theoretical result.

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What this paper is about

A superconvergence result is established in this article for approximate solutions of second-order elliptic equations by mixed finite element methods over quadrilaterals. The superconvergence indicates an accuracy of ${\cal O}(h^{k+2})$ for the mixed finite element approximation if the Raviart--Thomas or Brezzi--Douglas--Fortin--Marini elements of order k are employed with optimal error estimate of ${\cal O}(h^{k+1})$. Numerical experiments are presented to illustrate the theoretical result.

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Available abstract

A superconvergence result is established in this article for approximate solutions of second-order elliptic equations by mixed finite element methods over quadrilaterals. The superconvergence indicates an accuracy of ${\cal O}(h^{k+2})$ for the mixed finite element approximation if the Raviart--Thomas or Brezzi--Douglas--Fortin--Marini elements of order k are employed with optimal error estimate of ${\cal O}(h^{k+1})$. Numerical experiments are presented to illustrate the theoretical result.

Key concepts: Superconvergence, Quadrilateral, Mathematics, Finite element method, Mixed finite element method, Order (exchange), Mathematical analysis, Applied mathematics

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