An extension on the a-posterior error analysis for the finite element method
Gabriel N. Gatica (1987)
Extracta Mathematicae
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Gabriel N. Gatica (1987)
Extracta Mathematicae
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Karel Segeth (1993)
Applications of Mathematics
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The adjustment of one-dimensional space grid for a parabolic partial differential equation solved by the finite element method of lines is considered in the paper. In particular, the approach based on a posteriori error indicators and error estimators is studied. A statement on the rate of convergence of the approximation of error by estimator to the error in the case of a system of parabolic equations is presented.
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...
Valdman, Jan (2009)
Advances in Numerical Analysis
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Serge Nicaise, Nadir Soualem (2005)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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The paper presents an a posteriori error estimator for a (piecewise linear) nonconforming finite element approximation of the heat equation in , or 3, using backward Euler’s scheme. For this discretization, we derive a residual indicator, which use a spatial residual indicator based on the jumps of normal and tangential derivatives of the nonconforming approximation and a time residual indicator based on the jump of broken gradients at each time step. Lower and upper bounds form the...
W. Woolsey Johnson (1893)
Bulletin of the New York Mathematical Society
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Zakaria Belhachmi (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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We consider a non-conforming stabilized domain decomposition technique for the discretization of the three-dimensional Laplace equation. The aim is to extend the numerical analysis of residual error indicators to this model problem. Two formulations of the problem are considered and the error estimators are studied for both. In the first one, the error estimator provides upper and lower bounds for the energy norm of the mortar finite element solution whereas in the second case, it also...
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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