Bensaada, Mohammed, Esselaoui, Driss, Saramito, Pierre (2004)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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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...
Vlasák, Miloslav, Lamač, Jan
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We present an improvement to the direct flux reconstruction technique for equilibrated flux a posteriori error estimates for one-dimensional problems. The verification of the suggested reconstruction is provided by numerical experiments.
Burda, Pavel, Novotný, Jaroslav, Šístek, Jakub
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In computer fluid dynamics, employing stabilization to the finite element method is a commonly accepted way to improve the applicability of this method to high Reynolds numbers. Although the accompanying loss of accuracy is often referred, the question of quantifying this defect is still open. On the other hand, practitioners call for measuring the error and accuracy. In the paper, we present a novel approach for quantifying the difference caused by stabilization.
Vejchodský, Tomáš
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This paper presents a review of the complementary technique with the emphasis on computable and guaranteed upper bounds of the approximation error. For simplicity, the approach is described on a numerical solution of the Poisson problem. We derive the complementary error bounds, prove their fundamental properties, present the method of hypercircle, mention possible generalizations and show a couple of numerical examples.
S. Cochez-Dhondt, S. Nicaise, S. Repin (2009)
Mathematical Modelling of Natural Phenomena
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We present new a posteriori error estimates for the finite volume approximations of elliptic problems. They are obtained by applying functional a posteriori error estimates to natural extensions of the approximate solution and its flux computed by the finite volume method. The estimates give guaranteed upper bounds for the errors in terms of the primal (energy) norm, dual norm (for fluxes), and also in terms of the combined primal-dual norms. It is shown that the estimates provide sharp...