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Nonconforming elements in least-squares mixed finite element methods

Authors: Huo-Yuan Duan and Guo-Ping Liang
Journal: Math. Comp. 73 (2004), 1-18
MSC (2000): Primary 65N30
Published electronically: March 27, 2003
MathSciNet review: 2034108
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Abstract: In this paper we analyze the finite element discretization for the first-order system least squares mixed model for the second-order elliptic problem by means of using nonconforming and conforming elements to approximate displacement and stress, respectively. Moreover, on arbitrary regular quadrilaterals, we propose new variants of both the rotated ${\mathcal Q}_1$ nonconforming element and the lowest-order Raviart-Thomas element.

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Additional Information

Huo-Yuan Duan
Affiliation: Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, Peoples Republic of China

Guo-Ping Liang
Affiliation: Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, Peoples Republic of China

Keywords: Second-order elliptic problem, least-squares mixed finite element method, nonconforming element, normal continuous element
Received by editor(s): May 29, 2001
Received by editor(s) in revised form: May 7, 2002
Published electronically: March 27, 2003
Article copyright: © Copyright 2003 American Mathematical Society

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