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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...
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...
Sergey I. Repin, Tatiana S. Samrowski, Stéfan A. Sauter (2012)
ESAIM: Mathematical Modelling and Numerical Analysis
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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...
Sergey I. Repin, Tatiana S. Samrowski, Stéfan A. Sauter (2012)
ESAIM: Mathematical Modelling and Numerical Analysis
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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...
Sergey I. Repin, Tatiana S. Samrowski, Stéfan A. Sauter (2012)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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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...
Stephen Wainger (1969-1970)
Séminaire de théorie des nombres de Bordeaux
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