Virtual Element Methods for HJB Equations with Cordes Coefficients
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917748257325056 |
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| author | Cai, Ying Guo, Hailong Zhang, Zhimin |
| author_facet | Cai, Ying Guo, Hailong Zhang, Zhimin |
| contents | In this paper, we propose and analyze both conforming and nonconforming virtual element methods (VEMs) for the fully nonlinear second-order elliptic Hamilton-Jacobi-Bellman (HJB) equations with Cordes coefficients. By incorporating stabilization terms, we establish the well-posedness of the proposed methods, thus avoiding the need to construct a discrete Miranda-Talenti estimate. We derive the optimal error estimate in the discrete $H^2$ norm for both numerical formulations. Furthermore, a semismooth Newton's method is employed to linearize the discrete problems. Several numerical experiments using the lowest-order VEMs are provided to demonstrate the efficacy of the proposed methods and to validate our theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07153 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Virtual Element Methods for HJB Equations with Cordes Coefficients Cai, Ying Guo, Hailong Zhang, Zhimin Numerical Analysis In this paper, we propose and analyze both conforming and nonconforming virtual element methods (VEMs) for the fully nonlinear second-order elliptic Hamilton-Jacobi-Bellman (HJB) equations with Cordes coefficients. By incorporating stabilization terms, we establish the well-posedness of the proposed methods, thus avoiding the need to construct a discrete Miranda-Talenti estimate. We derive the optimal error estimate in the discrete $H^2$ norm for both numerical formulations. Furthermore, a semismooth Newton's method is employed to linearize the discrete problems. Several numerical experiments using the lowest-order VEMs are provided to demonstrate the efficacy of the proposed methods and to validate our theoretical results. |
| title | Virtual Element Methods for HJB Equations with Cordes Coefficients |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2408.07153 |