Abstract
In this paper, we present a posteriori error estimator for the nonconforming finite element approximation, including using Crouzeix-Raviart element and extended Crouzeix-Raviart element, of the Stokes eigenvalue problem. With the technique of Helmholtz decomposition, we first give out a posteriori error estimator and prove it as the global upper bound and local lower bound of the approximation error. Then, by deleting a jump term in the indicator, another simpler but equivalent indicator is obtained. Some numerical experiments are provided to verify our analysis.
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Supported by National Science Foundation of China (NSFC 91330202, 11001259, 11371026, 11201501, 11031006, 11071265, 2011CB309703, 2010DFR00700), the National Center for Mathematics and Interdisciplinary Science, CAS, the President Foundation of AMSS-CAS and the Program for Innovation Research in Central University of Finance and Economics
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Jia, S.H., Luo, F.S. & Xie, H.H. A posterior error analysis for the nonconforming discretization of Stokes eigenvalue problem. Acta. Math. Sin.-English Ser. 30, 949–967 (2014). https://doi.org/10.1007/s10114-014-3121-8
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DOI: https://doi.org/10.1007/s10114-014-3121-8