Work

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

Year: 2024

Type: article

Abstract: We propose and analyze an [Formula: see text]-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 [Formula: see text]. The analysis relies on the continuous Miranda–Talenti estimate for convex domains [Formula: see text] and is rather elementary. We prove stability and error estimates in [Formula: see text], including the effect of quadrature, under minimal regularity of the data. Numerical experiments illustrate the interplay of coefficient regularity and convergence rates in [Formula: see text].

Source: Mathematical Models and Methods in Applied Sciences

DOI: 10.1142/s0218202525500034

Authors: Guillaume Bonnet, Andrea Cangiani, Ricardo H. Nochetto