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Title: A continuous interior penalty finite element method for a third-order singularly perturbed boundary value problem

Abstract

We propose a continuous interior penalty finite element method designed for a third-order singularly perturbed problem. Using higher order polynomials on Shishkin-type layer-adapted meshes, a robust convergence has been proved in the corresponding energy norm. Moreover, we show numerical experiments which support our theoretical findings.

Authors:
 [1];  [2];  [3]
  1. University of Novi Sad, Department of Mathematics and Informatics, Faculty of Sciences (Serbia)
  2. Technical University of Dresden, Institute of Numerical Mathematics (Germany)
  3. University of Novi Sad, Department for Fundamental Disciplines, Faculty of Technical Sciences (Serbia)
Publication Date:
OSTI Identifier:
22769389
Resource Type:
Journal Article
Journal Name:
Computational and Applied Mathematics
Additional Journal Information:
Journal Volume: 37; Journal Issue: 1; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; BOUNDARY-VALUE PROBLEMS; CONVERGENCE; DIFFERENTIAL EQUATIONS; FINITE ELEMENT METHOD; POLYNOMIALS

Citation Formats

Zarin, Helena, Roos, Hans-Görg, and Teofanov, Ljiljana. A continuous interior penalty finite element method for a third-order singularly perturbed boundary value problem. United States: N. p., 2018. Web. doi:10.1007/S40314-016-0339-3.
Zarin, Helena, Roos, Hans-Görg, & Teofanov, Ljiljana. A continuous interior penalty finite element method for a third-order singularly perturbed boundary value problem. United States. doi:10.1007/S40314-016-0339-3.
Zarin, Helena, Roos, Hans-Görg, and Teofanov, Ljiljana. Thu . "A continuous interior penalty finite element method for a third-order singularly perturbed boundary value problem". United States. doi:10.1007/S40314-016-0339-3.
@article{osti_22769389,
title = {A continuous interior penalty finite element method for a third-order singularly perturbed boundary value problem},
author = {Zarin, Helena and Roos, Hans-Görg and Teofanov, Ljiljana},
abstractNote = {We propose a continuous interior penalty finite element method designed for a third-order singularly perturbed problem. Using higher order polynomials on Shishkin-type layer-adapted meshes, a robust convergence has been proved in the corresponding energy norm. Moreover, we show numerical experiments which support our theoretical findings.},
doi = {10.1007/S40314-016-0339-3},
journal = {Computational and Applied Mathematics},
issn = {0101-8205},
number = 1,
volume = 37,
place = {United States},
year = {2018},
month = {3}
}