Number of the records: 1
Flux reconstructions in the Lehmann-Goerisch method for lower bounds on eigenvalues
- 1.
SYSNO ASEP 0489966 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Flux reconstructions in the Lehmann-Goerisch method for lower bounds on eigenvalues Author(s) Vejchodský, Tomáš (MU-W) RID, SAI, ORCID Source Title Journal of Computational and Applied Mathematics. - : Elsevier - ISSN 0377-0427
Roč. 340, October 1 (2018), s. 676-690Number of pages 15 s. Language eng - English Country NL - Netherlands Keywords eigenproblem ; guaranteed ; finite element method Subject RIV BA - General Mathematics OECD category Pure mathematics Institutional support MU-W - RVO:67985840 UT WOS 000440264600046 EID SCOPUS 85046099786 DOI 10.1016/j.cam.2018.02.034 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2019
Number of the records: 1