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

We propose and analyze an H2-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 ≥ 2. The analysis relies on the continuous Miranda-Talenti estimate for convex domains ω and is rather elementary. We prove stability and error estimates in H2(ω), including the effect of quadrature, under minimal regularity of the data. Numerical experiments illustrate the interplay of coefficient regularity and convergence rates in H2(ω).