A dynamic mass transport method for Poisson-Nernst-Planck equations

A dynamic mass-transport method is proposed for approximately solving the Poisson–Nernst–Planck (PNP) equations. The semi-discrete scheme based on JKO type variational formulation naturally enforces solution positivity and energy law as continuous PNP system. fully discrete further formulated a constrained minimization problem, shown to be solvable, satisfy all three properties (mass conservation, dissipation) independent of time step size or spatial mesh size. Numerical experiments are conducted validate convergence computed solutions verify structure preserving property scheme.