  This article is an attempt to provide a self consistent picture, including
existence analysis and numerical solution algorithms, of the mathematical
problems arising from modeling photocurrent transients in Organic-polymer Solar
Cells (OSCs). The mathematical model for OSCs consists of a system of nonlinear
diffusion-reaction partial differential equations (PDEs) with electrostatic
convection, coupled to a kinetic ordinary differential equation (ODE). We
propose a suitable reformulation of the model that allows us to prove the
existence of a solution in both stationary and transient conditions and to
better highlight the role of exciton dynamics in determining the device turn-on
time. For the numerical treatment of the problem, we carry out a temporal
semi-discretization using an implicit adaptive method, and the resulting
sequence of differential subproblems is linearized using the Newton-Raphson
method with inexact evaluation of the Jacobian. Then, we use exponentially
fitted finite elements for the spatial discretization, and we carry out a
thorough validation of the computational model by extensively investigating the
impact of the model parameters on photocurrent transient times.
