Discrete advection–diffusion equations on graphs: Maximum principle and finite volumes
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F19%3A43955327" target="_blank" >RIV/49777513:23520/19:43955327 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.amc.2019.06.014" target="_blank" >https://doi.org/10.1016/j.amc.2019.06.014</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.amc.2019.06.014" target="_blank" >10.1016/j.amc.2019.06.014</a>
Alternative languages
Result language
angličtina
Original language name
Discrete advection–diffusion equations on graphs: Maximum principle and finite volumes
Original language description
We study an initial value problem for explicit and implicit difference advection–diffusion equations on graphs. Problems on both finite and infinite graphs are considered. We analyze the existence and uniqueness of solutions. Interestingly, we show that there exist infinitely many solutions to implicit problems on infinite graphs similarly as in the case of continuous or lattice diffusion equations on infinite spatial domains. The main part of the paper is devoted to maximum principles. Firstly, we establish discrete maximum principles for equations on graphs. Then we show that finite volume numerical schemes for advection–diffusion PDEs in any dimension can be reformulated as equations on graphs and consequently, we use this relation to verify maximum principles for corresponding numerical solutions.
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
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/LO1506" target="_blank" >LO1506: Sustainability support of the centre NTIS - New Technologies for the Information Society</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
APPLIED MATHEMATICS AND COMPUTATION
ISSN
0096-3003
e-ISSN
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Volume of the periodical
361
Issue of the periodical within the volume
15.11.2019
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
15
Pages from-to
630-644
UT code for WoS article
000474545500051
EID of the result in the Scopus database
2-s2.0-85067545331