Abstract
A Galerkin finite element scheme is used to provide flexible numerical solutions to the Poisson—Boltzmann equation for electrical double layers in one and two dimensions. A Newton sequence is used for the solution of the set of nonlinear equations arising from the finite element discretization procedure. Convergence of the Newton sequence is rapid, generally occurring in less than four iterations. Isoparametric finite elements are used for computational ease. Error analysis is applied to the solution of the linearized Poisson—Boltzmann equation (Debye—Hückel approximation) and also to the full iterative scheme. Numerical solutions are presented for (i) overlapping cylindrical and planar electrical double layers, and (ii) the overlapping electrical double layers of two interacting platelets.
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