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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2404.06490 |
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| _version_ | 1866910403711205376 |
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| author | Boyana, Satyajith Bommana Lewis, Thomas Liu, Sijing Zhang, Yi |
| author_facet | Boyana, Satyajith Bommana Lewis, Thomas Liu, Sijing Zhang, Yi |
| contents | In this paper, we propose and analyze a numerically stable and convergent scheme for a convection-diffusion-reaction equation in the convection-dominated regime. Discontinuous Galerkin (DG) methods are considered since standard finite element methods for the convection-dominated equation cause spurious oscillations. We choose to follow a novel DG finite element differential calculus framework introduced in Feng et al. (2016) and approximate the infinite-dimensional operators in the equation with the finite-dimensional DG differential operators. Specifically, we construct the numerical method by using the dual-wind discontinuous Galerkin (DWDG) formulation for the diffusive term and the average discrete gradient operator for the convective term along with standard DG stabilization. We prove that the method converges optimally in the convection-dominated regime. Numerical results are provided to support the theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06490 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence analysis of novel discontinuous Galerkin methods for a convection dominated problem Boyana, Satyajith Bommana Lewis, Thomas Liu, Sijing Zhang, Yi Numerical Analysis 65N30 In this paper, we propose and analyze a numerically stable and convergent scheme for a convection-diffusion-reaction equation in the convection-dominated regime. Discontinuous Galerkin (DG) methods are considered since standard finite element methods for the convection-dominated equation cause spurious oscillations. We choose to follow a novel DG finite element differential calculus framework introduced in Feng et al. (2016) and approximate the infinite-dimensional operators in the equation with the finite-dimensional DG differential operators. Specifically, we construct the numerical method by using the dual-wind discontinuous Galerkin (DWDG) formulation for the diffusive term and the average discrete gradient operator for the convective term along with standard DG stabilization. We prove that the method converges optimally in the convection-dominated regime. Numerical results are provided to support the theoretical findings. |
| title | Convergence analysis of novel discontinuous Galerkin methods for a convection dominated problem |
| topic | Numerical Analysis 65N30 |
| url | https://arxiv.org/abs/2404.06490 |