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.
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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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The research of C. Bi was partially supported by Shandong Province Natural Science Foundation (ZR2010AM004), Projects of Shandong Province Higher Educational Science and Technology Program (J10LA01, J11LA09), and the AMSS-PolyU Joint Research Institute for Engineering and Management Mathematics. The research of V. Ginting was partially supported by the grants from DOE (DE-FE0004832 and DE-SC0004982), the Center for Fundamentals of Subsurface Flow of the School of Energy Resources of the University of Wyoming (WYDEQ49811GNTG, WYDEQ49811PER), and from NSF (DMS-1016283).
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Bi, C., Ginting, V. A Posteriori Error Estimates of Discontinuous Galerkin Method for Nonmonotone Quasi-linear Elliptic Problems. J Sci Comput 55, 659–687 (2013). https://doi.org/10.1007/s10915-012-9651-2
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DOI: https://doi.org/10.1007/s10915-012-9651-2