A Posteriori Estimates for Partial Differential Equations - download pdf or read online

By Repin, Sergey

ISBN-10: 3110191539

ISBN-13: 9783110191530

This ebook bargains with the trustworthy verification of the accuracy of approximate strategies that is one of many important difficulties in sleek utilized analysis. After giving an outline of the equipment constructed for types in line with partial differential equations, the writer derives computable a posteriori errors estimates through the use of tools of the speculation of partial differential equations and useful research. those estimates are appropriate to approximate suggestions computed by way of a variety of tools.

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Extra info for A Posteriori Estimates for Partial Differential Equations (Radon Series on Computational and Applied Mathematics)

Example text

Ohnimus [339] and R. Verf¨urth [358, 360]. , in C. Carstensen, R. Klose, and A. Orlando [97]. Finally, we note that implicit type methods are often used for the indication of local errors. Concerning a posteriori methods developed to evaluate local errors of FEM approximations, we address the reader to the books by M. Ainsworth and T. Oden [8] and I. Babuˇska and T. Strouboulis [35]. Also we recommend papers by I. Babuˇska, F. Ihlenburg, A. Mathur, T. Strouboulis, S. K. Gangaraj, C. S. Upadhyay [27, 39, 39, 37], E.

Homogeneous Laplace equation in a rectangular domain) it is possible to construct such approximations but for problems with strongly nonhomogeneous coefficients in complicated domains, vector-valued problems, problems with nonlinear and convective terms this task is much more difficult. , see C. Johnson and B. Mercier [188]) are constructed by means of macroelements. Sometimes, numerical analysts use “almost equilibrated” approximations that may not exactly satisfy the differential relation. 2) is not guaranteed.

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. , in M. Kˇr´ızˇ ek and P. Neittaanm¨aki [201], J. R. Whiteman and G. Goodsell [370], and in the book [200]. Equilibration.

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A Posteriori Estimates for Partial Differential Equations (Radon Series on Computational and Applied Mathematics) by Repin, Sergey


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