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 ra...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2024-02-01
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| Series: | Mathematical Modelling and Analysis |
| Subjects: | |
| Online Access: | https://jau.vgtu.lt/index.php/MMA/article/view/16979 |
| Summary: | 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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| ISSN: | 1392-6292 1648-3510 |