Finite element method on Shishkin mesh for a singularly perturbed problem with an interior layer

Zhang, Jin; Ma, Xiaoqi; Lv, Yanhui

doi:10.1016/j.aml.2021.107509

Cited by 10 publications

(2 citation statements)

References 15 publications

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“…Proof According to the arguments in Zhang et al [29, Theorem 2], the proof of Theorem 2 can be obtained easily. □…”

Section: A Priori Informationmentioning

confidence: 99%

“…For these interior layer models, researchers usually adopt finite difference methods to analyze their convergence, such as previous studies [6, 26–28]. In Zhang et al [29], we have proved a uniform convergence of optimal order for an interior layer problem by using a finite element method. However, at present, we have not come across a paper that deals with interior layer problems by using SDFEMs.…”

Section: Introductionmentioning

confidence: 97%

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Streamline diffusion finite element method for a singularly perturbed problem with an interior layer on Shishkin mesh

Zhang

2023

Math Methods in App Sciences

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With the continuous development of science and technology, singularly perturbed problems have attracted more and more attentions from computational fluid scholars. In this paper, we discuss a singularly perturbed convection–diffusion problem with a discontinuous convection. Generally speaking, due to this discontinuity, an interior layer appears in the solution. A streamline diffusion finite element method on Shishkin mesh is used to solve this problem, and the optimal order of convergence in a modified streamline diffusion norm is derived. Numerical results are presented to support the theoretical conclusion.

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“…Proof According to the arguments in Zhang et al [29, Theorem 2], the proof of Theorem 2 can be obtained easily. □…”

Section: A Priori Informationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Streamline diffusion finite element method for a singularly perturbed problem with an interior layer on Shishkin mesh

Zhang

2023

Math Methods in App Sciences

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NIPG Method on Shishkin Mesh for Singularly Perturbed Convection-Diffusion Problem with Discontinuous Convection Coefficient

Ranjan¹,

Gowrisankar²

2023

Lecture Notes in Networks and Systems

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Supercloseness of the NIPG method for a singularly perturbed convection diffusion problem on Shishkin mesh

Zhang,

2024

Calcolo

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Finite element method on Shishkin mesh for a singularly perturbed problem with an interior layer

Cited by 10 publications

References 15 publications

Streamline diffusion finite element method for a singularly perturbed problem with an interior layer on Shishkin mesh

Streamline diffusion finite element method for a singularly perturbed problem with an interior layer on Shishkin mesh

NIPG Method on Shishkin Mesh for Singularly Perturbed Convection-Diffusion Problem with Discontinuous Convection Coefficient

Supercloseness of the NIPG method for a singularly perturbed convection diffusion problem on Shishkin mesh

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