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Erschienen in: Journal of Applied Mathematics and Computing 1-2/2021

10.09.2020 | Original Research

A unified study on superconvergence analysis of Galerkin FEM for singularly perturbed systems of multiscale nature

verfasst von: Maneesh Kumar Singh, Gautam Singh, Srinivasan Natesan

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2021

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Abstract

We discuss the superconvergence analysis of the Galerkin finite element method for the singularly perturbed coupled system of both reaction–diffusion and convection–diffusion types. The superconvergence study is carried out by using linear finite element, and it is shown to be second-order (up to a logarithmic factor) uniformly convergent in the suitable discrete energy norm. We have conducted some numerical experiments for the system of reaction–diffusion and system of convection–diffusion models, which validate the theoretical results.

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Metadaten
Titel
A unified study on superconvergence analysis of Galerkin FEM for singularly perturbed systems of multiscale nature
verfasst von
Maneesh Kumar Singh
Gautam Singh
Srinivasan Natesan
Publikationsdatum
10.09.2020
Verlag
Springer Berlin Heidelberg
Erschienen in
Journal of Applied Mathematics and Computing / Ausgabe 1-2/2021
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-020-01434-4

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