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Flux reconstructions in the Lehmann-Goerisch method for lower bounds on eigenvalues
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SYSNO ASEP 0489966 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Flux reconstructions in the Lehmann-Goerisch method for lower bounds on eigenvalues Tvůrce(i) Vejchodský, Tomáš (MU-W) RID, SAI, ORCID Zdroj.dok. Journal of Computational and Applied Mathematics. - : Elsevier - ISSN 0377-0427
Roč. 340, October 1 (2018), s. 676-690Poč.str. 15 s. Jazyk dok. eng - angličtina Země vyd. NL - Nizozemsko Klíč. slova eigenproblem ; guaranteed ; finite element method Vědní obor RIV BA - Obecná matematika Obor OECD Pure mathematics Institucionální podpora MU-W - RVO:67985840 UT WOS 000440264600046 EID SCOPUS 85046099786 DOI 10.1016/j.cam.2018.02.034 Anotace The standard application of the Lehmann-Goerisch method for lower bounds on eigenvalues of symmetric elliptic second-order partial differential operators relies on determination of fluxes. These fluxes are usually computed by solving a global saddle point problem. In this paper we propose a simpler global problem that yields these fluxes of the same quality. The simplified problem is smaller, it is positive definite, and any H(div) conforming finite elements, such as Raviart-Thomas elements, can be used for its solution. In addition, these global problems can be split into a number of independent local problems on patches, which allows for trivial parallelization. The computational performance of these approaches is illustrated by numerical examples for Laplace and Steklov type eigenvalue problems. These examples also show that local flux reconstructions enable computation of lower bounds on eigenvalues on considerably finer meshes than the traditional global reconstructions. Pracoviště Matematický ústav Kontakt Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Rok sběru 2019
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