Error estimates for a fully discrete $\varepsilon-$uniform finite element method on quasi uniform meshes
| Autor: | Srinivasan Natesan, Ali Şendur, Gautam Singh |
|---|---|
| Přispěvatelé: | ALKÜ, Fakülteler, Eğitim Fakültesi, Matematik ve Fen Bilimleri Eğitimi Bölümü, ALKÜ, Enstitüler, Lisansüstü Eğitim Enstitüsü, Matematik ve Fen Bilimleri Eğitimi Ana Bilim Dalı |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Matematik Algebra and Number Theory Uniform convergence Piecewise-Uniform Shishkin Mesh Mathematical analysis Finite element method Mathematics::Numerical Analysis Computer Science::Graphics Uniform Convergence Boundary Layers Finite Element Method singularly perturbed convection-diffusion-reaction boundary-value problem finite element method boundary layers piecewise-uniform Shishkin mesh uniform convergence Polygon mesh Singularly Perturbed Convection-Diffusion-Reaction Boundary-Value Problem Geometry and Topology Analysis Mathematics |
| Zdroj: | Volume: 50, Issue: 5 1306-1324 Hacettepe Journal of Mathematics and Statistics |
| ISSN: | 2651-477X |
| Popis: | 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 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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