Adapted Lie splitting method for convection-diffusion problems with singular convective term
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910421704769536 |
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| author | Dang, Thi Tam Hoang, Trung Hau Orlandi, Giandomenico |
| author_facet | Dang, Thi Tam Hoang, Trung Hau Orlandi, Giandomenico |
| contents | Splitting methods are a widely used numerical scheme for solving convection-diffusion problems. However, they may lose stability in some situations, particularly when applied to convection-diffusion problems in the presence of an unbounded convective term. In this paper, we propose a new splitting method, called the "Adapted Lie splitting method", which successfully overcomes the observed instability in certain cases. Assuming that the unbounded coefficient belongs to a suitable Lorentz space, we show that the adapted Lie splitting converges to first-order under the analytic semigroup framework. Furthermore, we provide numerical experiments to illustrate our newly proposed splitting approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15947 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Adapted Lie splitting method for convection-diffusion problems with singular convective term Dang, Thi Tam Hoang, Trung Hau Orlandi, Giandomenico Numerical Analysis Splitting methods are a widely used numerical scheme for solving convection-diffusion problems. However, they may lose stability in some situations, particularly when applied to convection-diffusion problems in the presence of an unbounded convective term. In this paper, we propose a new splitting method, called the "Adapted Lie splitting method", which successfully overcomes the observed instability in certain cases. Assuming that the unbounded coefficient belongs to a suitable Lorentz space, we show that the adapted Lie splitting converges to first-order under the analytic semigroup framework. Furthermore, we provide numerical experiments to illustrate our newly proposed splitting approach. |
| title | Adapted Lie splitting method for convection-diffusion problems with singular convective term |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2404.15947 |