Nonconforming elements in least-squares mixed finite element methods

Duan, Huo-Yuan; Liang, Guo-Ping

doi:10.1090/S0025-5718-03-01520-5

Nonconforming elements in least-squares mixed finite element methods
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by Huo-Yuan Duan and Guo-Ping Liang PDF

Math. Comp. 73 (2004), 1-18 Request permission

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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