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Numerical Study Of A One-Dimensional Poisson-Nernst–Planck Ion Channel Model By Finite Element Backward And Forward Euler Methods, Michel Stanislas Korfhage

Theses and Dissertations

This thesis presents a numerical study of a one-dimensional Poisson-Nernst-Planck (PNP) ion channel model,which describes the transport of charged species in an electrolyte under the influence of an electric field. We develop a new numerical scheme for solving the PNP model by combining the method of lines with the finite element and Euler's forward and backward methods. We then implement the scheme based on the finite element library from the FEniCS project. To validate the accuracy of our numerical scheme, we construct an analytical solution of the PNP model with source terms. We find in numerical tests that the backward …