Virtual Element Methods for HJB Equations with Cordes Coefficients
<|reference_start|>Virtual Element Methods for HJB Equations with Cordes Coefficients: 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.<|reference_end|>
@article{cai2024virtual,
    title={Virtual Element Methods for HJB Equations with Cordes Coefficients},
    author={Ying Cai, Hailong Guo, Zhimin Zhang},
    journal={arXiv preprint arXiv:2408.07153},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.07153},
    primaryClass={math.NA cs.NA}
}