B. Achchab, M. El Fatini, A. Souissi (2010)
Mathematical Modelling of Natural Phenomena
Similarity:
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
Hannukainen, Antti, Korotov, Sergey
Similarity:
The paper is devoted to the problem of reliable control of accuracy of approximate solutions obtained in computer simulations. This task is strongly related to the so-called a posteriori error estimates, giving computable bounds for computational errors and detecting zones in the solution domain, where such errors are too large and certain mesh refinements should be performed. Mathematical model described by a linear elliptic (reaction-diffusion) equation with mixed boundary conditions...
Ibrahim Cheddadi, Radek Fučík, Mariana I. Prieto, Martin Vohralík (2009)
ESAIM: Mathematical Modelling and Numerical Analysis
Similarity:
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...
Koichi Niijima (1989/90)
Numerische Mathematik
Similarity:
Sergey I. Repin, Tatiana S. Samrowski, Stéfan A. Sauter (2012)
ESAIM: Mathematical Modelling and Numerical Analysis
Similarity:
We consider linear elliptic problems with variable coefficients, which may sharply change values and have a complex behavior in the domain. For these problems, a new combined discretization-modeling strategy is suggested and studied. It uses a sequence of simplified models, approximating the original one with increasing accuracy. Boundary value problems generated by these simplified models are solved numerically, and the approximation and modeling errors are estimated by estimates of...