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A simple approach to reliable and robust a posteriori error estimation for singularly perturbed problems
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SYSNO ASEP 0505170 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title A simple approach to reliable and robust a posteriori error estimation for singularly perturbed problems Author(s) Ainsworth, M. (US)
Vejchodský, Tomáš (MU-W) RID, SAI, ORCIDSource Title Computer Methods in Applied Mechanics and Engineering. - : Elsevier - ISSN 0045-7825
Roč. 353, 15 August (2019), s. 373-390Number of pages 18 s. Language eng - English Country CH - Switzerland Keywords finite element analysis ; singularly perturbed problems ; flux reconstruction Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GA18-09628S GA ČR - Czech Science Foundation (CSF) Method of publishing Limited access Institutional support MU-W - RVO:67985840 UT WOS 000470960700017 EID SCOPUS 85066256085 DOI 10.1016/j.cma.2019.05.014 Annotation A simple flux reconstruction for finite element solutions of reaction-diffusion problems is shown to yield fully computable upper bounds on the energy norm of error in an approximation of singularly perturbed reaction-diffusion problem. The flux reconstruction is based on simple, independent post-processing operations over patches of elements in conjunction with standard Raviart-Thomas vector fields. We prove that the corresponding local error indicators are locally efficient and robust (up to a nonstandard oscillation term) with respect to any mesh size and any size of the reaction coefficient, including the singularly perturbed limit. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2020 Electronic address http://dx.doi.org/10.1016/j.cma.2019.05.014
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