Implicit extended discontinuous Galerkin scheme for solving singularly perturbed Burgers' equations
We present the implicit-modal discontinuous Galerkin scheme for solving the coupled viscous and singularly perturbed Burgers’ equations. This scheme overcomes overshoot and undershoots phenomena in the singularly perturbed Burgers’ equations. We present the stability analysis and obtain suitable ran...
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| Published in | Mathematical modelling and analysis Vol. 29; no. 1; pp. 1 - 22 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Vilnius
Vilnius Gediminas Technical University
22.02.2024
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1392-6292 1648-3510 1648-3510 |
| DOI | 10.3846/mma.2024.16979 |
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| Abstract | We present the implicit-modal discontinuous Galerkin scheme for solving the coupled viscous and singularly perturbed Burgers’ equations. This scheme overcomes overshoot and undershoots phenomena in the singularly perturbed Burgers’ equations. We present the stability analysis and obtain suitable ranges for penalty terms and time steps. Also, we gain the constant of trace inequality for the approximate function and its first derivatives based on Legendre basis functions. The numerical results have good agreement with the analytical and available approximate solutions. |
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| AbstractList | We present the implicit-modal discontinuous Galerkin scheme for solving the coupled viscous and singularly perturbed Burgers’ equations. This scheme overcomes overshoot and undershoots phenomena in the singularly perturbed Burgers’ equations. We present the stability analysis and obtain suitable ranges for penalty terms and time steps. Also, we gain the constant of trace inequality for the approximate function and its first derivatives based on Legendre basis functions. The numerical results have good agreement with the analytical and available approximate solutions. We present the implicit-modal discontinuous Galerkin scheme for solving the coupled viscous and singularly perturbed Burgers' equations. This scheme overcomes overshoot and undershoots phenomena in the singularly perturbed Burgers' equations. We present the stability analysis and obtain suitable ranges for penalty terms and time steps. Also, we gain the constant of trace inequality for the approximate function and its first derivatives based on Legendre basis functions. The numerical results have good agreement with the analytical and available approximate solutions. Keywords: discontinuous Galerkin method, backward Euler method, viscous Burgers' equation, singularly perturbed Burgers' equation, stability analysis. AMS Subject Classification: 65M60; 35K67; 35K15. |
| Audience | Academic |
| Author | Mondanizadeh, Maryam Khodayari-Samghabadi, Samaneh Momeni-Masuleh, Sayed Hodjatollah |
| Author_xml | – sequence: 1 givenname: Samaneh surname: Khodayari-Samghabadi fullname: Khodayari-Samghabadi, Samaneh organization: Department of Mathematics, Shahed University, P.O. Box 18151-159, Tehran, Iran – sequence: 2 givenname: Maryam surname: Mondanizadeh fullname: Mondanizadeh, Maryam organization: Department of Mathematics, Shahed University, P.O. Box 18151-159, Tehran, Iran – sequence: 3 givenname: Sayed Hodjatollah orcidid: 0000-0002-4481-2751 surname: Momeni-Masuleh fullname: Momeni-Masuleh, Sayed Hodjatollah organization: Department of Mathematics, Shahed University, P.O. Box 18151-159, Tehran, Iran |
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| Copyright | Copyright (c) 2024 The Author(s). Published by Vilnius Gediminas Technical University. COPYRIGHT 2024 Vilnius Gediminas Technical University 2024. This work is published under https://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
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| Snippet | We present the implicit-modal discontinuous Galerkin scheme for solving the coupled viscous and singularly perturbed Burgers’ equations. This scheme overcomes... We present the implicit-modal discontinuous Galerkin scheme for solving the coupled viscous and singularly perturbed Burgers' equations. This scheme overcomes... |
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| SubjectTerms | backward Euler method Basis functions Burgers equation discontinuous Galerkin method Functions, Discontinuous Functions, Implicit Galerkin method Laplace transforms Ordinary differential equations Perturbation (Mathematics) Polynomials singularly perturbed Burgers’ equation Stability analysis Tests, problems and exercises viscous Burgers’ equation |
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| Title | Implicit extended discontinuous Galerkin scheme for solving singularly perturbed Burgers' equations |
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