A Non-Consistent Virtual Element Method for Reaction Diffusion Equations

Abstract

A simple virtual element method, avoiding the traditional enhancement technique, is used for numerical solution of a reaction-diffusion problem in the lowest order cases $k$ = 1 and 2. Optimal error estimates are established in $H^1$ and $L^2$ norms. Numerical results are consistent with theoretical findings but show that for $k$ ≥ 3 the method is not optimal.