Conforming virtual element method for nondivergence form linear elliptic equations with Cordes coefficients
<|reference_start|>Conforming virtual element method for nondivergence form linear elliptic equations with Cordes coefficients: We propose and analyze an $H^2$-conforming Virtual Element Method (VEM) for the simplest linear elliptic PDEs in nondivergence form with Cordes coefficients. The VEM hinges on a hierarchical construction valid for any dimension $d \ge 2$. The analysis relies on the continuous Miranda-Talenti estimate for convex domains $\Omega$ and is rather elementary. We prove stability and error estimates in $H^2(\Omega)$, including the effect of quadrature, under minimal regularity of the data. Numerical experiments illustrate the interplay of coefficient regularity and convergence rates in $H^2(\Omega)$.<|reference_end|>
@article{bonnet2024conforming,
    title={Conforming virtual element method for nondivergence form linear elliptic
  equations with Cordes coefficients},
    author={Guillaume Bonnet, Andrea Cangiani and Ricardo H. Nochetto},
    journal={arXiv preprint arXiv:2404.08442},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.08442},
    primaryClass={math.NA cs.NA}
}