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Model. Anal. Inform. Sist., 2016, Volume 23, Number 3, Pages 357–363 (Mi mais506)  

Error estimates in balanced norms of finite element methods on Shishkin meshes for reaction-diffusion problems

H.-G. Roos

Institut für Numerische Mathematik, Technische Universität Dresden, 01062 Dresden, Deutschland

Abstract: Error estimates of finite element methods for reaction-diffusion problems are often realized in the related energy norm. In the singularly perturbed case, however, this norm is not adequate. A different scaling of the $H^1$ seminorm leads to a balanced norm which reflects the layer behavior correctly.

Keywords: singular perturbation, supercloseness, combination technique, balanced norms.

DOI: https://doi.org/10.18255/1818-1015-2016-3-357-363

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UDC: 519.6
Received: 20.05.2016
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Citation: H.-G. Roos, “Error estimates in balanced norms of finite element methods on Shishkin meshes for reaction-diffusion problems”, Model. Anal. Inform. Sist., 23:3 (2016), 357–363

Citation in format AMSBIB
\Bibitem{Roo16}
\by H.-G.~Roos
\paper Error estimates in balanced norms of finite element methods on Shishkin meshes for reaction-diffusion problems
\jour Model. Anal. Inform. Sist.
\yr 2016
\vol 23
\issue 3
\pages 357--363
\mathnet{http://mi.mathnet.ru/mais506}
\crossref{https://doi.org/10.18255/1818-1015-2016-3-357-363}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3520858}
\elib{http://elibrary.ru/item.asp?id=26246302}


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