Virtual element method for semilinear elliptic problems on polygonal meshes

Abstract

In this paper, the virtual element method is employed to approximate semilinear elliptic problems over arbitrary polygonal meshes. The nonlinear load term is approximated by employing the orthogonal L2 projection. The finite dimensional formulation and its implementation are discussed in detail and optimal a priori error estimate in H1 norm is derived. Further, two numerical experiments are conducted in order to illustrate the performance of the proposed scheme and to numerically justify the theoretical convergence rate. It is observed that the proposed method yields optimal convergence rates in both L2 and H1 norm.