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Dvoparametarski singularno perturbovani konturni problemi na mrežama različitog tipa

Singularly perturbed boundary value problems with two parameters on various meshes

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2016
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Author
Brdar, Mirjana
Mentor
Zarin, Helena
Teofanov, Ljiljana
Committee members
Herceg, Dragoslav
Zarin, Helena
Teofanov, Ljiljana
Uzelac, Zorica
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Abstract
U tezi se istražuje uniformna konvergencija Galerkinovog postupka konačnih elemenata na mrežama različitog tipa za dvoparametarske singularno perturbovane probleme. Uvedene su slojno-adaptivne mreže za probleme konvekcije-reakcije-difuzije:  Bahvalovljeva, Duran-Šiškinova i Duranova za jednodimenzionalni i Duran-Šiškinova i Duranova mreža za dvodimenzionalni problem. Za pomenute probleme na svim ovim mrežama analizirane su greške interpolacije, diskretizacije i greška u energetskoj normi i dokazana je uniformna konvergencija Galerkinovog postupka konačnih elemenata. Sva teorijska tvrđenja su potvrđena numeričkim eksperimentima.  
The thesis explores the uniform convergence for Galerkin nite element method on various meshes for two parameter singularly perturbed problems. Layer-adapted meshes are introduced for convection-reaction-diusion problems: Bakhvalov, Duran-Shishkin and Duran meshes for a one dimensional and Duran-Shishkin and Duran meshes for a two dimensional problem. We analyze the errors of interpolation, discretization and error in the energy norm and prove the parameter uniform convergence for Galerkin nite element method on mentioned meshes. Numerical experiments support theoretical ndings.  
Faculty:
University of Novi Sad, Faculty of Science
Date:
27-05-2016
Keywords:
Singularno perturbovani problemi / Singularly perturbed problems / two small parameters / Bakhvalov / Duran and Duran-Shishkin meshes / finite element method / uniform convergence. / dva mala parametra / Bahvalovljeva / Duranova i Duran-Šiškinova mreža / postupak konačnih elemenata / uniformna konvergencija.
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http://www.cris.uns.ac.rs/DownloadFileServlet/Disertacija145820865154725.pdf?controlNumber=(BISIS)100302&fileName=145820865154725.pdf&id=5100&source=NaRDuS&language=sr
http://nardus.mpn.gov.rs/handle/123456789/5495
http://www.cris.uns.ac.rs/record.jsf?recordId=100302&source=NaRDuS&language=sr
http://www.cris.uns.ac.rs/DownloadFileServlet/IzvestajKomisije145820867726211.pdf?controlNumber=(BISIS)100302&fileName=145820867726211.pdf&id=5101&source=NaRDuS&language=sr

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