Journal of Scientific Computing

, Volume 55, Issue 3, pp 659–687 | Cite as

A Posteriori Error Estimates of Discontinuous Galerkin Method for Nonmonotone Quasi-linear Elliptic Problems

Article

Abstract

In this paper, we propose and study the residual-based a posteriori error estimates of h-version of symmetric interior penalty discontinuous Galerkin method for solving a class of second order quasi-linear elliptic problems which are of nonmonotone type. Computable upper and lower bounds on the error measured in terms of a natural mesh-dependent energy norm and the broken H 1-seminorm, respectively, are derived. Numerical experiments are also provided to illustrate the performance of the proposed estimators.

Keywords

Quasi-linear elliptic problems Discontinuous Galerkin method A posteriori error estimates 

Notes

Acknowledgements

The authors wish to express their deepest gratitude to the anonymous referees who generously shared their insight and perspectives on the subject of this paper.

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of MathematicsYantai UniversityShandongP.R. China
  2. 2.Department of MathematicsUniversity of WyomingLaramieUSA

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