Convergence of the multiplicative Schwarz method for singularly perturbed convection-diffusion problems discretized on a Shishkin mesh
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10384902" target="_blank" >RIV/00216208:11320/18:10384902 - isvavai.cz</a>
Alternative codes found
RIV/67985807:_____/18:00500540
Result on the web
<a href="https://doi.org/10.1553/etna_vol48s40" target="_blank" >https://doi.org/10.1553/etna_vol48s40</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1553/etna_vol48s40" target="_blank" >10.1553/etna_vol48s40</a>
Alternative languages
Result language
angličtina
Original language name
Convergence of the multiplicative Schwarz method for singularly perturbed convection-diffusion problems discretized on a Shishkin mesh
Original language description
We analyze the convergence of the multiplicative Schwarz method applied to nonsymmetric linear algebraic systems obtained from discretizations of one-dimensional singularly perturbed convection-diffusion equations by upwind and central finite differences on a Shishkin mesh. Using the algebraic structure of the Schwarz iteration matrices we derive bounds on the infinity norm of the error that are valid from the first step of the iteration. Our bounds for the upwind scheme prove rapid convergence of the multiplicative Schwarz method for all relevant choices of parameters in the problem. The analysis for the central difference is more complicated, since the submatrices that occur are nonsymmetric and sometimes even fail to be M-matrices. Our bounds still prove the convergence of the method for certain parameter choices.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GC17-04150J" target="_blank" >GC17-04150J: Reliable two-scale Fourier/finite element-based simulations: Error-control, model reduction, and stochastics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Electronic Transactions on Numerical Analysis
ISSN
1068-9613
e-ISSN
—
Volume of the periodical
48
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
23
Pages from-to
40-62
UT code for WoS article
000459295400003
EID of the result in the Scopus database
2-s2.0-85053523947