Displaying similar documents to “On the numerical performance of a sharp a posteriori error estimator for some nonlinear elliptic problems”

Implicit a posteriori error estimation using patch recovery techniques

Tamás Horváth, Ferenc Izsák (2012)

Open Mathematics

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We develop implicit a posteriori error estimators for elliptic boundary value problems. Local problems are formulated for the error and the corresponding Neumann type boundary conditions are approximated using a new family of gradient averaging procedures. Convergence properties of the implicit error estimator are discussed independently of residual type error estimators, and this gives a freedom in the choice of boundary conditions. General assumptions are elaborated for the gradient...

Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods

Linda El Alaoui, Alexandre Ern (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We analyze residual and hierarchical a posteriori error estimates for nonconforming finite element approximations of elliptic problems with variable coefficients. We consider a finite volume box scheme equivalent to a nonconforming mixed finite element method in a Petrov–Galerkin setting. We prove that all the estimators yield global upper and local lower bounds for the discretization error. Finally, we present results illustrating the efficiency of the estimators, for instance, in the...