A Virtual Element Method For Two-Dimensional Steady-State Poisson-Nernst-Planck Equations

Poisson-Nernst-Planck(PNP)equations are widely used in biomolecules,semi-conductors and other fields.The virtual element method is a kind of discretization method of partial differential equations developed in recent years.It has advantages of strong mesh adaptability and wide application,and has attracted more and more researchers' interest.The PNP equations have characteristics such as nonlinear cou-pling,etc.,which make it difficult to study the error estimation theory of the virtual element method.In this thesis,a suitable virtual element discretization form is presented for a class of two-dimensional steady-state PNP equations.Next,by treating the terms such as nonlinear coupling carefully,the H1 norm error estimate theory is estab-lished both for the linear and quadratic virtual element method solutions.Then,a Fortran90 program is developed to solve the PNP equations which are discretized by the virtual element method under general polygonal meshes.The numerical results show that the effectiveness of the virtual element method for PNP equations and verify the correctness of the theoretical results.