Nonconforming virtual element method for general second-order elliptic problems on curved domain

Abstract

The nonconforming virtual element method with curved edges was proposed and analyzed for the Poisson equation by L. Beirão da Veiga, Y. Liu, L. Mascotto, and A. Russo in (J. Sci. Comput. 99(1) 2024). The goal of this paper is to extend the nonconforming virtual element method to a more general second-order elliptic problem with variable coefficients in domains with curved boundaries and curved internal interfaces. We prove an optimal convergence of arbitrary order in the energy and \(L^2\)-norms, confirmed by numerical experiments on a set of polygonal meshes. The accuracy of the numerical approximation provided by the method is shown to be comparable with that obtained from the theoretical analysis.