Error estimates for a fully discrete epsilon-uniform finite element method on quasi uniform meshes

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dc.contributor.authorŞendur, Ali
dc.contributor.authorNatesan, Srinivasan
dc.contributor.authorSingh, Gautam
dc.date.accessioned2022-09-14T13:21:41Z
dc.date.available2022-09-14T13:21:41Z
dc.date.issued2021
dc.departmentALKÜ, Enstitüler, Lisansüstü Eğitim Enstitüsü, Matematik ve Fen Bilimleri Eğitimi Ana Bilim Dalı
dc.description.abstractIn this article, we analyze a fully discrete epsilon-uniformly convergent finite element method for singularly perturbed convection-diffusion-reaction boundary-value problems, on piecewise-uniform meshes. Here, we choose L-splines as basis functions. We will concentrate on the convergence analysis of the finite element method which employ the discrete L-spline basis functions instead of their continuous counterparts. The L-splines are approximated on the piecewise-uniform Shishkin mesh inside each element. These approximations are used as basis functions in the frame of Galerkin FEM on a coarse piecewise-uniform mesh to discretize the domain. Further, we determine the amount of error introduced by the discrete L-spline basis functions in the overall numerical method, and explore the possibility of recovering the order of convergence that are consistent with the classical order of convergence for the numerical methods using the exact L-splines.
dc.identifier.doi10.15672/hujms.691017
dc.identifier.endpage1324en_US
dc.identifier.issue5en_US
dc.identifier.startpage1306en_US
dc.identifier.urihttps://hdl.handle.net/20.500.12868/1620
dc.identifier.urihttps://dergipark.org.tr/en/pub/hujms/issue/65430/691017
dc.identifier.volume50en_US
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.language.isoen
dc.relation.ispartofHacettepe Journal of Mathematics and Statistics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectsingularly perturbed convection-diffusion-reaction boundary-value problem
dc.subjectFinite element method
dc.subjectBoundary layers
dc.subjectPiecewise-uniform Shishkin mesh
dc.subjectUniform convergence
dc.titleError estimates for a fully discrete epsilon-uniform finite element method on quasi uniform meshes
dc.typeArticle

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