IMPLICIT EXTENDED DISCONTINUOUS GALERKIN SCHEME FOR SOLVING SINGULARLY PERTURBED BURGERS' EQUATIONS-Reference-Cited by-同舟云学术

IMPLICIT EXTENDED DISCONTINUOUS GALERKIN SCHEME FOR SOLVING SINGULARLY PERTURBED BURGERS' EQUATIONS

Published:2024-02-22 Issue:1 Volume:29 Page:1-22
ISSN:1392-6292
Container-title:Mathematical Modelling and Analysis
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Author:

Khodayari-Samghabadi Samaneh¹,Mondanizadeh Maryam¹,Momeni-Masuleh Sayed Hodjatollah¹^ORCID

Affiliation:

1. Department of Mathematics, Shahed University, P.O. Box 18151-159, Tehran, Iran

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.

Publisher

Vilnius Gediminas Technical University

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