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Title: | Singularly perturbed boundary value problems with two parameters on various meshes Dvoparametarski singularno perturbovani konturni problemi na mrežama različitog tipa |
Authors: | Brdar Mirjana | Keywords: | Singularly perturbed problems, two small parameters, Bakhvalov, Duran and Duran-Shishkin meshes, finite element method,uniform convergence.;Singularno perturbovani problemi, dva mala parametra, Bahvalovljeva,Duranova i Duran-Šiškinova mreža, postupak konačnih elemenata,uniformna konvergencija. | Issue Date: | 27-May-2016 | Publisher: | Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu University of Novi Sad, Faculty of Sciences at Novi Sad |
Abstract: | <p>U tezi se istražuje uniformna konvergencija Galerkinovog postupka konačnih elemenata na mrežama različitog tipa za dvoparametarske singularno perturbovane probleme.</p><p>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.<br /> </p> <p>The thesis explores the uniform convergence for Galerkin nite element<br />method on various meshes for two parameter singularly perturbed problems.<br />Layer-adapted meshes are introduced for convection-reaction-diusion<br />problems: Bakhvalov, Duran-Shishkin and Duran meshes for a one dimensional<br />and Duran-Shishkin and Duran meshes for a two dimensional problem.<br />We analyze the errors of interpolation, discretization and error in the energy<br />norm and prove the parameter uniform convergence for Galerkin nite element<br />method on mentioned meshes. Numerical experiments support theoretical<br />ndings.<br /> </p> |
URI: | https://open.uns.ac.rs/handle/123456789/16726 |
Appears in Collections: | PMF Teze/Theses |
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