Error analysis of virtual element method for the Poisson–Boltzmann equation

Abstract The Poisson–Boltzmann equation, which incorporates the source of the Dirac distribution, has been widely applied in predicting the electrostatic potential of biomolecular systems in solution. In this paper we discuss and analyse the virtual element method for the Poisson–Boltzmann equation on general polyhedral meshes. Nearly optimal error estimates, approaching the best possible accuracy, are achieved for the virtual element approximation in both the L 2 -norm and H 1 -norm, even when the solution of the entire domain has low regularity. The efficiency of the virtual element method and the validity of the proposed theoretical prediction are confirmed through numerical experiments conducted on various polyhedral meshes.