B. Achchab, M. El Fatini, A. Souissi (2010)
Mathematical Modelling of Natural Phenomena
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We derive a residual a posteriori error estimates for the subscales stabilization of convection diffusion equation. The estimator yields upper bound on the error which is global and lower bound that is local
Ibrahim Cheddadi, Radek Fučík, Mariana I. Prieto, Martin Vohralík (2009)
ESAIM: Mathematical Modelling and Numerical Analysis
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We derive error estimates for singularly perturbed reaction–diffusion problems which yield a guaranteed upper bound on the discretization error and are fully and easily computable. Moreover, they are also locally efficient and robust in the sense that they represent local lower bounds for the actual error, up to a generic constant independent in particular of the reaction coefficient. We present our results in the framework of the vertex-centered finite volume method but their nature...
Vejchodský, Tomáš
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The equilibrated residual method and the method of hypercircle are popular methods for a posteriori error estimation for linear elliptic problems. Both these methods are intended to produce guaranteed upper bounds of the energy norm of the error, but the equilibrated residual method is guaranteed only theoretically. The disadvantage of the hypercircle method is its globality, hence slowness. The combination of these two methods leads to local, hence fast, and guaranteed a posteriori...