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Adaptive Finite-Element Solution of the Nonlinear Poisson–Boltzmann Equation: A Charged Spherical Particle at Various Distances from a Charged Cylindrical Pore in a Charged Planar Surface

1997; Elsevier BV; Volume: 187; Issue: 2 Linguagem: Inglês

10.1006/jcis.1996.4705

1095-7103

W. Richard Bowen, Adel O. Sharif,

Composite Material Mechanics

A Galerkin finite-element approach combined with an error estimator and automatic mesh refinement has been used to provide a flexible numerical solution of the Poisson–Boltzmann equation. A Newton sequence technique was used to solve the nonlinear equations arising from the finite-element discretization procedure. Errors arising from the finite-element solution due to mesh refinement were calculated using the Zienkiewicz–Zhu error estimator, and an automatic remeshing strategy was adopted to achieve a solution satisfying a preset quality. Examples of the performance of the error estimator in adaptive mesh refinement are presented. The adaptive finite-element scheme presented in this study has proved to be an effective technique in minimizing errors in finite-element solutions for a given problem, in particular those of complex geometries. As an example, numerical solutions are presented for the case of a charged spherical particle at various distances from a charged cylindrical pore in a charged planar surface. Such a scheme provides a quantification of the significance of electrostatic interactions for an important industrial technology—membrane separation processes.