Abstract
Two residual-based a posteriori error estimators of the nonconforming Crouzeix-Raviart element are derived for elliptic problems with Dirac delta source terms. One estimator is shown to be reliable and efficient, which yields global upper and lower bounds for the error in piecewise W 1,p-seminorm. The other one is proved to give a global upper bound of the error in L p-norm. By taking the two estimators as refinement indicators, adaptive algorithms are suggested, which are experimentally shown to attain optimal convergence orders.
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This work was supported in part by the National Natural Science Foundation of China (Grant No. 10771150), the National Basic Research Program of China (Grant No. 2005CB321701), and the Program for New Century Excellent Talents in University (Grant No. NCET-07-0584)
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Du, S., Xie, X. Residual-based a posteriori error estimates of nonconforming finite element method for elliptic problems with Dirac delta source terms. Sci. China Ser. A-Math. 51, 1440–1460 (2008). https://doi.org/10.1007/s11425-008-0113-0
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DOI: https://doi.org/10.1007/s11425-008-0113-0