Adaptive numerical method for Poisson–Boltzmann equation and its application Original Research Article

The adaptive mesh refinement procedure for a finite-element solution of the Poisson–Boltzmann equation is briefly described. The final mesh is a Delaunay triangulation and is optimal in the sense that all the cells provide close values of errors. The procedure allows the gradual improvement of the solution and adjustment of the geometry of the problem. The performance of the proposed approach is illustrated by applying it to three problems of colloidal interaction: two free identical particles, two identical particles confined in a charged cylindrical pore, and a particle near a charged plane. A new model of the boundary conditions for numerical studies of colloidal particles is introduced.