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arXiv · 2404.08442

Conforming virtual element method for nondivergence form linear elliptic equations with Cordes coefficients

Guillaume Bonnet·Andrea Cangiani·Ricardo H. Nochetto
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Abstract

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 $H^2(\Omega)$.

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Guillaume Bonnet, Andrea Cangiani, Ricardo H. Nochetto. 2024-04-12. Conforming virtual element method for nondivergence form linear elliptic equations with Cordes coefficients. https://arxiv.org/abs/2404.08442

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