Guaranteed Two-Sided Bounds on All Eigenvalues of Preconditioned Diffusion and Elasticity Problems Solved By the Finite Element Method
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F21%3A00344873" target="_blank" >RIV/68407700:21110/21:00344873 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.21136/AM.2020.0217-19" target="_blank" >https://doi.org/10.21136/AM.2020.0217-19</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.21136/AM.2020.0217-19" target="_blank" >10.21136/AM.2020.0217-19</a>
Alternative languages
Result language
angličtina
Original language name
Guaranteed Two-Sided Bounds on All Eigenvalues of Preconditioned Diffusion and Elasticity Problems Solved By the Finite Element Method
Original language description
A method of characterizing all eigenvalues of a preconditioned discretized scalar diffusion operator with Dirichlet boundary conditions has been recently introduced in Gergelits, Mardal, Nielsen, and Strakoš (2019). Motivated by this paper, we offer a slightly different approach that extends the previous results in some directions. Namely, we provide bounds on all increasingly ordered eigenvalues of a general diffusion or elasticity operator with tensor data, discretized with the conforming finite element method, and preconditioned by the inverse of a matrix of the same operator with different data. Our results hold for mixed Dirichlet and Robin or periodic boundary conditions applied to the original and preconditioning problems. The bounds are two-sided, guaranteed, easily accessible, and depend solely on the material data.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Applications of mathematics
ISSN
0862-7940
e-ISSN
1572-9109
Volume of the periodical
2020
Issue of the periodical within the volume
1
Country of publishing house
CZ - CZECH REPUBLIC
Number of pages
22
Pages from-to
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UT code for WoS article
000584991300002
EID of the result in the Scopus database
2-s2.0-85094189227