Quasi-Norm Local Error Estimators for p-Laplacian

In this paper, we extend the quasi-norm techniques used in a priori error estimation of finite element approximation of degenerate nonlinear systems in order to carry out an improved a posteriori error analysis for the p-Laplacian. We derive quasi-norm a posteriori error estimators of residual type, which are shown to provide improved upper and lower bounds on the discretization error. For sufficiently regular solutions, these estimators are further shown to be equivalent on the discretization error in a quasi norm. Numerical results demonstrating these a posteriori estimators are also presented.