Journal of Scientific Computing

, Volume 74, Issue 1, pp 23–48 | Cite as

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

Article

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.

Keywords

Two-grid finite element method Nonlinear elliptic problems A posteriori error estimates 

Mathematics Subject Classification

65N15 65N30 

Notes

Acknowledgements

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

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of MathematicsYantai UniversityShandongChina
  2. 2.School of Mathematical SciencesTongji UniversityShanghaiChina
  3. 3.Department of Applied MathematicsThe Hong Kong Polytechnic UniversityHung HomChina

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