Adaptive Mesh Enrichment for the Poisson–Boltzmann Equation

An adaptive mesh enrichment procedure for a finite-element solution of the two-dimensional Poisson–Boltzmann equation is described. The mesh adaptation is performed by subdividing the cells using information obtained in the previous step of the solution and next rearranging the mesh to be a Delaunay triangulation. The procedure allows the gradual improvement of the quality of the solution and adjustment of the geometry of the problem. The performance of the proposed approach is illustrated by applying it to the problem of two identical colloidal particles in a symmetric electrolyte.