Convergent finite difference schemes for stochastic transport equations
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909464707203072 |
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| author | Fjordholm, Ulrik S. Karlsen, Kenneth H. Pang, Peter H. C. |
| author_facet | Fjordholm, Ulrik S. Karlsen, Kenneth H. Pang, Peter H. C. |
| contents | We present difference schemes for stochastic transport equations with low-regularity velocity fields. We establish $L^2$ stability and convergence of the difference approximations under conditions that are less strict than those required for deterministic transport equations. The $L^2$ estimate, crucial for the analysis, is obtained through a discrete duality argument and a comprehensive examination of a class of backward parabolic difference schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_02208 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Convergent finite difference schemes for stochastic transport equations Fjordholm, Ulrik S. Karlsen, Kenneth H. Pang, Peter H. C. Numerical Analysis Analysis of PDEs 60H15, 65M12, 60H50, 65M80 We present difference schemes for stochastic transport equations with low-regularity velocity fields. We establish $L^2$ stability and convergence of the difference approximations under conditions that are less strict than those required for deterministic transport equations. The $L^2$ estimate, crucial for the analysis, is obtained through a discrete duality argument and a comprehensive examination of a class of backward parabolic difference schemes. |
| title | Convergent finite difference schemes for stochastic transport equations |
| topic | Numerical Analysis Analysis of PDEs 60H15, 65M12, 60H50, 65M80 |
| url | https://arxiv.org/abs/2309.02208 |