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A new a posteriori error estimate for the Morley element

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Abstract

In this paper, we present a posteriori error analysis for the nonconforming Morley element of the fourth order elliptic equation. We propose a new residual-based a posteriori error estimator and prove its reliability and efficiency. These results refine those of Beirao da Veiga et al. (Numer Math 106:165–179, 2007) by dropping two edge jump terms in both the energy norm of the error and the estimator, and those of Wang and Zhang (Local a priori and a posteriori error estimates of finite elements for biharmonic equation, Research Report, 13, 2006) by showing the efficiency in the sense of Verfürth (A review of a posteriori error estimation and adaptive mesh-refinement techniques, Wiley-Teubner, New York, 1996). Moreover, the normal component in the estimators of Beirao da Veiga et al. (Numer Math 106:165–179, 2007) and Wang and Zhang (Local a priori and a posteriori error estimates of finite elements for biharmonic equation, Research Report, 13, 2006) is dropped, and therefore only the tangential component of the stress on each edge comes into the estimator. In addition, we generalize these results to three dimensional case.

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Authors and Affiliations

  1. LMAM and School of Mathematical Sciences, Peking University, 100871, Beijing, People’s Republic of China

    Jun Hu

  2. Institute of Computational Mathematics, Chinese Academy of Sciences, 100080, Beijing, People’s Republic of China

    Zhongci Shi

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  1. Jun Hu
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  2. Zhongci Shi
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Correspondence to Jun Hu.

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Hu, J., Shi, Z. A new a posteriori error estimate for the Morley element. Numer. Math. 112, 25–40 (2009). https://doi.org/10.1007/s00211-008-0205-3

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