A new a posteriori error estimate for the Morley element |
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Authors: | Jun Hu Zhongci Shi |
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Institution: | (1) LMAM and School of Mathematical Sciences, Peking University, 100871 Beijing, People’s Republic of China;(2) Institute of Computational Mathematics, Chinese Academy of Sciences, 100080 Beijing, People’s Republic of China |
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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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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 65N10 65N15 35J25 |
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