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...
Sergey Grosman (2006)
ESAIM: Mathematical Modelling and Numerical Analysis
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Singularly perturbed reaction-diffusion problems exhibit in general solutions with anisotropic features, strong boundary and/or interior layers. This anisotropy is reflected in a discretization by using meshes with anisotropic elements. The quality of the numerical solution rests on the robustness of the error estimator with respect to both, the perturbation parameters of the problem and the anisotropy of the mesh. The equilibrated residual method has been shown to provide one of...