A Péclet-robust discontinuous Galerkin method for nonlinear diffusion with advection
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914679849222144 |
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| author | da Veiga, Lourenço Beirão Di Pietro, Daniele A. Haile, Kirubell B. |
| author_facet | da Veiga, Lourenço Beirão Di Pietro, Daniele A. Haile, Kirubell B. |
| contents | We analyze a Discontinuous Galerkin method for a problem with linear advection-reaction and $p$-type diffusion, with Sobolev indices $p\in (1, \infty)$. The discretization of the diffusion term is based on the full gradient including jump liftings and interior-penalty stabilization while, for the advective contribution, we consider a strengthened version of the classical upwind scheme. The developed error estimates track the dependence of the local contributions to the error on local Péclet numbers. A set of numerical tests supports the theoretical derivations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09814 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Péclet-robust discontinuous Galerkin method for nonlinear diffusion with advection da Veiga, Lourenço Beirão Di Pietro, Daniele A. Haile, Kirubell B. Numerical Analysis We analyze a Discontinuous Galerkin method for a problem with linear advection-reaction and $p$-type diffusion, with Sobolev indices $p\in (1, \infty)$. The discretization of the diffusion term is based on the full gradient including jump liftings and interior-penalty stabilization while, for the advective contribution, we consider a strengthened version of the classical upwind scheme. The developed error estimates track the dependence of the local contributions to the error on local Péclet numbers. A set of numerical tests supports the theoretical derivations. |
| title | A Péclet-robust discontinuous Galerkin method for nonlinear diffusion with advection |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2402.09814 |