Journal of Scientific Computing

, Volume 55, Issue 3, pp 659–687

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


DOI: 10.1007/s10915-012-9651-2

Cite this article as:
Bi, C. & Ginting, V. J Sci Comput (2013) 55: 659. doi:10.1007/s10915-012-9651-2


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 H1-seminorm, respectively, are derived. Numerical experiments are also provided to illustrate the performance of the proposed estimators.


Quasi-linear elliptic problemsDiscontinuous Galerkin methodA posteriori error estimates

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