Year: 2018
Author: Chuanmiao Chen, Jing Yang
International Journal of Numerical Analysis and Modeling, Vol. 15 (2018), Iss. 1-2 : pp. 102–110
Abstract
The singularity-separated method (SSM) for the singular perturbation problem $-\epsilon u''+bu' + cu = f(x), u(0) = u(1) = 0$, is proposed for the first time. The solution is expressed as $u = w-ν$, where $w$ is the solution of corresponding third boundary value problem and $ν$ is an exact singular function. We have proved a global regularity, $||w||_2 ≤ C$, where the constant $C$ is independent of $\epsilon$, and discussed three kinds of finite element (FE) methods with SSM. Numerical results show that these FE-solutions have the high accuracy when only one element in boundary layer is taken.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2018-IJNAM-10558
International Journal of Numerical Analysis and Modeling, Vol. 15 (2018), Iss. 1-2 : pp. 102–110
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 9
Keywords: Singular perturbation problem singularity-separated method third boundary value second order regularity finite elements.