Download A posteriori estimates for partial differential equations by Repin, Sergey PDF

By Repin, Sergey

This ebook offers with the trustworthy verification of the accuracy of approximate suggestions that's one of many important difficulties in glossy utilized research. After giving an outline of the tools built for types according to partial differential equations, the writer derives computable a posteriori errors estimates through the use of equipment of the idea of partial differential equations and sensible research. those estimates Read more...

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Equilibration. Another group of methods exploits differential relations (usually they follow from conservation laws), which for exact solutions must be exactly satisfied. 2) and set U D Qf . , div qh Cf D 0 ), then this method provides a guaranteed upper bound of the error. This property is lost if qh is equilibrated approximately but usually ruh qh serves as a good error indicator provided that qh is sufficiently close to the set of equilibrated fields. g, M. Ainsworth and J. T. Oden [8], D. W.

2) For this problem, we derive two-sided a posteriori estimates with the help of two different methods. The first method uses variational arguments, the second one is based on transformations of the corresponding integral identity. We discuss properties of the estimates, their practical implementation, and relationships between them and a posteriori estimates of other types. v/ D jrvj f v dx: v2V0 2 Henceforth, we call it Problem P . rv; y/ D y2Y 1 2 jyj f v 2 Ã dx; where Y D L2 . ; Rd /. x/. 2.

Ruchovets [256] and M. Zl´amal [385, 386]. , to J. -S. Chow, G. F. Carey and R. D. Lazarov [106], R. E. Ewing, R. D. Lazarov and J. Wang [130], I. Hlav´ac˘ ek and M. K˘ri˘zek [176], M. Kˇr´ızˇ ek and P. Neittaanm¨aki [202, 242], R. Lazarov [217], R. Verf¨urth [356], J. Wang [367], J. Wang and X. -E. Wiberg, F. Abdulwahab and S. Ziukas [371], Z. Zhang and A. Naga [377], and in many other publications. In L. Wahlbin [366] readers can find a detailed exposition of the subject and other references.

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