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Calcolo
Published in: Calcolo 3/2018

01-09-2018

Analysis of the SDFEM for singularly perturbed differential–difference equations

Authors: Li-Bin Liu, Haitao Leng, Guangqing Long

Published in: Calcolo | Issue 3/2018

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Abstract

In this paper, the stability and accuracy of a streamline diffusion finite element method (SDFEM) for the singularly perturbed differential–difference equation of convection term with a small shift is considered. With a special choice of the stabilization quadratic bubble function and by using the discrete Green’s function, the new method is shown to have an optimal second order in the sense that \(\Vert u-u_{h}\Vert _{\infty }\le C\inf \nolimits _{v_h\in V^h}\Vert u-v_{h}\Vert _{\infty }\), where \(u_{h}\) is the SDFEM approximation of the exact solution u in linear finite element space \(V_{h}\). At last, a second order uniform convergence result for the SDFEM is obtained. Numerical results are given to confirm the \(\varepsilon \)-uniform convergence rate of the nodal errors.
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Metadata
Title
Analysis of the SDFEM for singularly perturbed differential–difference equations
Authors
Li-Bin Liu
Haitao Leng
Guangqing Long
Publication date
01-09-2018
Publisher
Springer International Publishing
Published in
Calcolo / Issue 3/2018
Print ISSN: 0008-0624
Electronic ISSN: 1126-5434
DOI
https://doi.org/10.1007/s10092-018-0265-4

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