Adaptive finite element approximation for steady-state Poisson-Nernst-Planck equations

In this paper, we develop an adaptive finite element method for the nonlinear steady-state Poisson-Nernst-Planck equations, where spatial adaptivity geometrical singularities and boundary layer effects are mainly considered. As a key contribution, equations studied systematically rigorous analysis residual-based posteriori error estimate of system is presented. With regularity linearized derived by taking G-derivatives system, show robust relationship between solution estimator. Numerical experiments given to validate efficiency estimator demonstrate expected rate convergence. further tests, mesh refinements successfully observed.