New $C^0$ interior penalty method for Monge-Ampère equations
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917765901713408 |
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| author | Chu, Tianyang Guo, Hailong Zhang, Zhimin |
| author_facet | Chu, Tianyang Guo, Hailong Zhang, Zhimin |
| contents | Monge-Ampère equation is a prototype second-order fully nonlinear partial differential equation. In this paper, we propose a new idea to design and analyze the $C^0$ interior penalty method to approximation the viscosity solution of the Monge-Ampère equation. The new methods is inspired from the discrete Miranda-Talenti estimate. Based on the vanishing moment representation, we approximate the Monge-Ampère equation by the fourth order semi-linear equation with some additional boundary conditions. We will use the discrete Miranda-Talenti estimates to ensure the well-posedness of the numerical scheme and derive the error estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00434 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New $C^0$ interior penalty method for Monge-Ampère equations Chu, Tianyang Guo, Hailong Zhang, Zhimin Numerical Analysis Monge-Ampère equation is a prototype second-order fully nonlinear partial differential equation. In this paper, we propose a new idea to design and analyze the $C^0$ interior penalty method to approximation the viscosity solution of the Monge-Ampère equation. The new methods is inspired from the discrete Miranda-Talenti estimate. Based on the vanishing moment representation, we approximate the Monge-Ampère equation by the fourth order semi-linear equation with some additional boundary conditions. We will use the discrete Miranda-Talenti estimates to ensure the well-posedness of the numerical scheme and derive the error estimates. |
| title | New $C^0$ interior penalty method for Monge-Ampère equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2409.00434 |