Some a Posteriori Error Estimators for p-Laplacian Based on Residual Estimation or Gradient Recovery
Journal of Scientific Computing
A posteriori error estimates for control problems governed by nonlinear elliptic equations
Applied Numerical Mathematics - Special issue: 2nd international workshop on numerical linear algebra, numerical methods for partial differential equations and optimization
SIAM Journal on Numerical Analysis
Numerical comparison of nonlinear subgridscale models via adaptive mesh refinement
Mathematical and Computer Modelling: An International Journal
Mathematical and Computer Modelling: An International Journal
Calcolo: a quarterly on numerical analysis and theory of computation
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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.