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https://open.uns.ac.rs/handle/123456789/26330| Title: | Postupci konačnih elemenata za singularno perturbovane probleme i prekidi Finite ('lenient methods for singularly perturbed problems with special emphasis on discontinuities |
Authors: | Zarin Helena | Keywords: | singularnc perturbacije, granični sloj, unutrašnji sloj, postupak konačnih elemenata, diskontinualni postupci Galerkina. adaptivna mreža, uniformna konvergencija;singular perturbation, boundary layer, interior layer, finite element melliod. discontinuous Galerkin method, layer-adapted mesh, uniform convergence | Issue Date: | 19-Sep-2003 | 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 istražuju primene postupaka konačnili elemenata i adaptivnih mreža radi poboljšanja tačnosti približnih rešenja određenih singularno perturbovanih problema.<br />U jednodimenzionalnom slučaju se posmatraju problemi sa unutrašnjim slojevima koji su nastali zbog prekidnih polaznih funkcija. Pokazano je da stabilizovani postupci konačnih elemenata na mrežama Shishkinovog tipa uspešno rešavaju ovakve probleme, nezavisno od pert urbacionog parametra. Pri numeričkom rešavanju dvodimenzionalnih singularno perturbovanih problema koriste se diskontinualni postupci Galerkina. Za nesimetričnu verziju sa unutrašnjim kaznenim članovi­ ma na anizotropnoj Shishkinovoj mreži utvrđena je robustnost ovog postupka, posebno analizi rajući probleme reakcije-difuzije, odnosno konvekcije-difuzije sa regularnim i/ili paraboli-<br />čilim slojevima</p> <p>The thesis mainly explores applications of the finite element methods and layer-adapted meshes to improve the accuracy of approximate solutions of certain singular perturbation problems. In one-dimensional case, the problems with interior layers caused from discontinuous data are considered. It is proved that stabilized finite element methods on Shishkin-type meshes successfully resolve these problems independently of a perturbation parameter. The numerical treatment of two-dimensional singularly perturbed problems involves discontin­uous Galerkin finite element methods. The robustness of a nonsymmetric version with interior penalties on anisotropic Shishkin mesh is established for reaction-diffusion and convection-diffusion problems with regular and/or parabolic, layers</p> |
URI: | https://open.uns.ac.rs/handle/123456789/26330 |
| Appears in Collections: | PMF Teze/Theses |
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