On Peter's Formula for Probable Error.
W. Woolsey Johnson (1893)
Bulletin of the New York Mathematical Society
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W. Woolsey Johnson (1893)
Bulletin of the New York Mathematical Society
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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...
Gabriel N. Gatica (1987)
Extracta Mathematicae
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M. V. Ćelić (1989)
Matematički Vesnik
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Shiina, Kumiko, Suzuki, Kenjiro (1999)
Journal for Geometry and Graphics
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Vejchodský, Tomáš
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The equilibrated residual method and the method of hypercircle are popular methods for a posteriori error estimation for linear elliptic problems. Both these methods are intended to produce guaranteed upper bounds of the energy norm of the error, but the equilibrated residual method is guaranteed only theoretically. The disadvantage of the hypercircle method is its globality, hence slowness. The combination of these two methods leads to local, hence fast, and guaranteed a posteriori...
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.
Karel Tříska (1933)
Aktuárské vědy
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