  The Poisson-Boltzmann equation is a nonlinear elliptic equation with Dirac
distribution sources, which has been widely applied to the prediction of
electrostatics potential of biological biomolecular systems in solution. In
this paper, we discuss and analysis the virtual element method for the
Poisson-Boltzmann equation on general polyhedral meshes. Under the low
regularity of the solution of the whole domain, nearly optimal error estimates
in both L2-norm and H1-norm for the virtual element approximation are obtained.
The numerical experiment on different polyhedral meshes shows the efficiency of
the virtual element method and verifies the proposed theoretical prediction.
