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A Novel Hierarchial Error Estimate for Elliptic Obstacle Problems

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Abstract

We present and analyze a novel hierarchical a posteriori error estimate for elliptic obstacle problems. The main result is that the energy norm of the finite element approximate error is, up to some extra oscillation term, equivalent to an appropriate hierarchical estimator. The proof is based upon some new observations on efficiency and some technical tools deriving from a previous work (Zou et al. in Numer. Math. 117:653–677, 2011). Moreover, we present an equivalence between the energy norm and the energy functional of the finite element approximate error. Several numerical experiments validate our theoretical findings.

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Acknowledgement

The author gratefully acknowledges Prof. Ralf Kornhuber for his suggestions on the research topic and Prof. Zhimin Zhang for his suggestions which leads to a significant improvement of the paper.

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Authors and Affiliations

  1. Department of Scientific Computation and Computers’ Applications, Sun Yat-sen University, Guangzhou, 510275, China

    Qingsong Zou

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  1. Qingsong Zou
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Correspondence to Qingsong Zou.

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This work is supported in part by NSFC under the grant 11171359.

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Zou, Q. A Novel Hierarchial Error Estimate for Elliptic Obstacle Problems. J Sci Comput 54, 77–96 (2013). https://doi.org/10.1007/s10915-012-9605-8

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