A posteriori error estimates of adaptive discontinuous Galerkin methods for monotone quasi-linear elliptic problems
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Liming Guo, Qingmin Zhang
A new residual-based a posteriori error estimator is proposed and analyzed for an incomplete interior penalty Galerkin discretization of monotone quasi-linear elliptic problems. We derive the computable upper and lower bounds on the error measured in an energy norm. It is proved that the estimator may have the same form as the continuous Galerkin finite element methods. Results of numerical example are presented.
Incomplete interior penalty Galerkin, A posteriori error estimator, Quasi-linear elliptic problems.