Error estimates for a fully discrete epsilon-uniform finite element method on quasi uniform meshes
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Tarih
2021
Yazarlar
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Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
In 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.
Açıklama
Anahtar Kelimeler
singularly perturbed convection-diffusion-reaction boundary-value problem, Finite element method, Boundary layers, Piecewise-uniform Shishkin mesh, Uniform convergence
Kaynak
Hacettepe Journal of Mathematics and Statistics
WoS Q Değeri
Q3
Scopus Q Değeri
Cilt
50
Sayı
5
