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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2024

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

Résumé

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 $H^2(\Omega)$.

Dates et versions

hal-04547532 , version 1 (15-04-2024)

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Guillaume Bonnet, Andrea Cangiani, Ricardo H. Nochetto. Conforming virtual element method for nondivergence form linear elliptic equations with Cordes coefficients. 2024. ⟨hal-04547532⟩
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