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

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.