Finite element error estimates for nonlinear convective problems

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10331078" target="_blank" >RIV/00216208:11320/16:10331078 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1515/jnma-2015-0030" target="_blank" >http://dx.doi.org/10.1515/jnma-2015-0030</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/jnma-2015-0030" target="_blank" >10.1515/jnma-2015-0030</a>

Result language
angličtina
Original language name
Finite element error estimates for nonlinear convective problems
Original language description
This paper is concerned with the analysis of the finite element method applied to a nonstationary nonlinear convective problem. Using special estimates of the convective terms, we prove a priori error estimates for an explicit, semidiscrete and implicit scheme. While the explicit case is rather straightforward via mathematical induction, for the semidiscrete scheme we need to apply so-called continuous mathematical induction and a nonlinear Gronwall lemma. For the implicit scheme, we use a suitable continuation of the discrete implicit solution and again use continuous mathematical induction to prove the error estimates. Finally, we extend the presented analysis from globally Lipschitz-continuous convective nonlinearities to the locally Lipschitz-continuous case.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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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)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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