Unconditionally positivity preserving and energy dissipative schemes for Poisson–Nernst–Planck equations

We develop a set of numerical schemes for the Poisson–Nernst–Planck equations. prove that our are mass conservative, uniquely solvable and keep positivity unconditionally. Furthermore, first-order scheme is proven to be unconditionally energy dissipative. These properties hold various spatial discretizations. Numerical results presented validate these properties. Moreover, indicate second-order also dissipative, both first- preserves maximum principle cases where equation satisfies principle.