Error estimates for a fully discrete varepsilon?uniform finite element methodon quasi uniform meshes
Yükleniyor...
Tarih
2021
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
In this article, we analyze a fully discrete varepsilon?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 thefinite element methodwhich employ the discreteL?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 meshto discretize the domain. Further, we determinethe 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 usingthe exact L?splines.
Açıklama
Anahtar Kelimeler
Piecewise-Uniform Shishkin Mesh, Boundary Layers, Uniform Convergence, Singularly Perturbed Convection-Diffusion-Reaction Boundary-Value Problem, Finite Element Method
Kaynak
Hacettepe Journal of Matehematics and Statistics
WoS Q Değeri
Scopus Q Değeri
Cilt
50
Sayı
5
