Two-grid virtual element discretization of semilinear elliptic problem

Abstract

In this paper a two grid algorithm for semilinear elliptic problem based on virtual element method (VEM) discretization is proposed. With this new algorithm the solution of a semilinear elliptic problem on a fine grid is reduced to the solution of a semilinear elliptic problem on a much coarser grid, and the solution of a linear system on the fine grid. A priori error estimates in H1 and L2 norms are derived. Numerical experiments are carried out to illustrate the theoretical findings.