A posteriori error analysis of a non-consistent virtual element method for reaction diffusion equations

Abstract This paper proposes and analyzes the residual-type a posteriori error estimates for a non-consistent virtual element method (VEM) for reaction–diffusion equations. The reliability and efficiency of the a posteriori error bound are derived under a weak mesh assumption. The error estimators enable us to devise an adaptive VEM by means of the mesh refinement strategy with the one-hanging-node rule. Numerical experiments are in agreement with the theoretical results.