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A Posteriori Error Estimates of Two-Grid Finite Element Methods for Nonlinear Elliptic Problems

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Abstract

In this article, we study the residual-based a posteriori error estimates of the two-grid finite element methods for the second order nonlinear elliptic boundary value problems. Computable upper and lower bounds on the error in the \(H^1\)-norm are established. Numerical experiments are also provided to illustrate the performance of the proposed estimators.

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Acknowledgements

The authors would like to thank an anonymous referee for his (her) valuable suggestions leading to an improvement of this article.

Author information

Authors and Affiliations

  1. Department of Mathematics, Yantai University, Shandong, 264005, China

    Chunjia Bi

  2. School of Mathematical Sciences, Tongji University, Shanghai, 200092, China

    Cheng Wang

  3. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong, China

    Yanping Lin

Authors
  1. Chunjia Bi
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  2. Cheng Wang
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  3. Yanping Lin
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Corresponding author

Correspondence to Cheng Wang.

Additional information

The research of C. Bi was partially supported by the National Science Foundation of China under Grant 11571297 and Shandong Province Natural Science Foundation under Grant ZR2014AM003. The research of C. Wang was partially supported by the National Science Foundation of China under Grant 11101311. The research of Y. Lin was partially supported by GRF 15301714 of HKSAR.

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Bi, C., Wang, C. & Lin, Y. A Posteriori Error Estimates of Two-Grid Finite Element Methods for Nonlinear Elliptic Problems. J Sci Comput 74, 23–48 (2018). https://doi.org/10.1007/s10915-017-0422-y

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  • DOI: https://doi.org/10.1007/s10915-017-0422-y

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