Existence, Uniqueness, and a Comparison of Nonintrusive Methods for the Stochastic Nonlinear Poisson--Boltzmann Equation

Abstract

The stochastic nonlinear Poisson--Boltzmann equation describes the electrostatic potential in a random environment in the presence of free charges and has applications in many fields. We show the existence and uniqueness of the solution of this nonlinear model equation and investigate its regularity with respect to a random parameter. Three popular nonintrusive methods, a stochastic Galerkin method, a discrete projection method, and a collocation method, are presented for its numerical solution.