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A posteriori error estimators for locally conservative methods of nonlinear elliptic problems. (English) Zbl 1125.65098
The paper is concerned with the unified analysis of some implicit and explicit error estimators for a general class of locally conservative methods applied to nonlinear elliptic problems. The implicit error estimator is obtained by extending the equilibrated residual method to locally conservative methods an the explicit error estimators are derived by bounding implicit error estimator further from above. The analysis is based in the decomposition of the error into a conforming part and a nonconforming part. The reliability of the methods is established within a unified framework. The results are applied to three locally conservative methods: the P1 nonconforming finite element method, the interior penalty discontinuous Galerkin method and the local discontinuous Galerkin method.

##### MSC:
 65N15 Error bounds for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J65 Nonlinear boundary value problems for linear elliptic equations
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