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The Poisson-Boltzmann equation (PBE) is one important implicit solvent continuum model for calculating electrostatics of protein in ionic solvent. Several numerical algorithms and program packages have been developed but verification and comparison between them remains an interesting topic. In this paper, a PBE test model is presented for a protein in a spherical solute region, along with its analytical solution. It is then used to verify a PBE finite element solver and applied to a numerical comparison study between a finite element solver and a finite difference solver. Such a study demonstrates the importance of retaining the interface conditions in the development of PBE solvers.

A Poisson-Boltzmann Equation Test Model for Protein in Spherical Solute Region and its Applications