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Journal of Scientific Computing

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19-02-2016

Analysis of SDFEM on Shishkin Triangular Meshes and Hybrid Meshes for Problems with Characteristic Layers

Authors: Jin Zhang, Xiaowei Liu

Published in: Journal of Scientific Computing | Issue 3/2016

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Abstract

In this paper, we analyze the streamline diffusion finite element method (SDFEM) for a model singularly perturbed convection–diffusion equation on a Shishkin triangular mesh and hybrid meshes. Supercloseness property of \(u^I-u^N\) is obtained, where \(u^I\) is the interpolant of the solution u and \(u^N\) is the SDFEM’s solution. The analysis depends on novel integral inequalities for the diffusion and convection parts in the bilinear form. Furthermore, analysis on hybrid meshes shows that bilinear elements should be recommended for the exponential layer, not for the characteristic layer. Finally, numerical experiments support these theoretical results.

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Title: Analysis of SDFEM on Shishkin Triangular Meshes and Hybrid Meshes for Problems with Characteristic Layers
Authors: Jin Zhang
Xiaowei Liu
Publication date: 19-02-2016
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 3/2016
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-016-0180-2

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