Rudi Beck, Ralf Hiptmair, Ronald H. W. Hoppe, Barbara Wohlmuth (2000)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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Gerd Kunert (2001)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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Singularly perturbed problems often yield solutions with strong directional features, e.g. with boundary layers. Such anisotropic solutions lend themselves to adapted, anisotropic discretizations. The quality of the corresponding numerical solution is a key issue in any computational simulation. To this end we present a new robust error estimator for a singularly perturbed reaction–diffusion problem. In contrast to conventional estimators, our proposal is suitable for anisotropic finite...
Gabriel N. Gatica (1987)
Extracta Mathematicae
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Segeth, Karel
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A lot of papers and books analyze analytical a posteriori error estimates from the point of view of robustness, guaranteed upper bounds, global efficiency, etc. At the same time, adaptive finite element methods have acquired the principal position among algorithms for solving differential problems in many physical and technical applications. In this survey contribution, we present and compare, from the viewpoint of adaptive computation, several recently published error estimation procedures...
Abdelhaq El Jai, Houria Hamzaoui (2009)
International Journal of Applied Mathematics and Computer Science
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The purpose of this short paper is to provide original results related to the choice of the number of sensors and their supports for general distributed parameter systems. We introduce the notion of extended sensors and we show that the observation error decreases when the support of a sensor is widened. We also show that the observation error decreases when the number of sensors increases.
W. Woolsey Johnson (1893)
Bulletin of the New York Mathematical Society
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French, Donald A., Larsson, Stig, Nochetto, Ricardo H. (2001)
Computational Methods in Applied Mathematics
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B. Achchab, A. Agouzal, K. Bouihat (2010)
Mathematical Modelling of Natural Phenomena
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In this paper, a new a posteriori error estimator for nonconforming convection diffusion approximation problem, which relies on the small discrete problems solution in stars, has been established. It is equivalent to the energy error up to data oscillation without any saturation assumption nor comparison with residual estimator
Jan Brandts (1999)
Applications of Mathematics
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We will investigate the possibility to use superconvergence results for the mixed finite element discretizations of some time-dependent partial differential equations in the construction of a posteriori error estimators. Since essentially the same approach can be followed in two space dimensions, we will, for simplicity, consider a model problem in one space dimension.