Number of the records: 1

Fully computable robust a posteriori error bounds for singularly perturbed reaction-diffusion problems

SYSNO ASEP	0367487
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	Fully computable robust a posteriori error bounds for singularly perturbed reaction-diffusion problems
Author(s)	Ainsworth, M. (GB) Vejchodský, Tomáš (MU-W)_{RID, SAI, ORCID}
Source Title	Numerische Mathematik - ISSN 0029-599X Roč. 119, č. 2 (2011), s. 219-243
Number of pages	25 s.
Language	eng - English
Country	DE - Germany
Keywords	a posteriori error estimates ; singularly perturbed problems ; reaction-diffusion
Subject RIV	BA - General Mathematics
R&D Projects	IAA100760702 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR)
	GA102/07/0496 GA ČR - Czech Science Foundation (CSF)
CEZ	AV0Z10190503 - MU-W (2005-2011)
UT WOS	000297164000001
EID SCOPUS	80052667051
DOI	10.1007/s00211-011-0384-1
Annotation	A procedure for the construction of robust, upper bounds for the error in the finite element approximation of singularly perturbed reaction–diffusion problems was presented in Ainsworth and Babuška (SIAM J Numer Anal 36(2):331–353, 1999) which entailed the solution of an infinite dimensional local boundary value problem. It is not possible to solve this problem exactly and this fact was recognised in the above work where it was indicated that the limitation would be addressed in a subsequent article. We view the present work as fulfilling that promise and as completing the investigation begun in Ainsworth and Babuška (SIAM J Numer Anal 36(2):331–353, 1999) by removing the obligation to solve a local problem exactly. The resulting new estimator is indeed fully computable and the first to provide fully computable, robust upper bounds in the setting of singularly perturbed problems discretised by the finite element method.
Workplace	Mathematical Institute
Contact	Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757
Year of Publishing	2012

Number of the records: 1