  This work concerns the numerical solution of a coupled system of
self-consistent reaction-drift-diffusion-Poisson equations that describes the
macroscopic dynamics of charge transport in photoelectrochemical (PEC) solar
cells with reactive semiconductor and electrolyte interfaces. We present three
numerical algorithms, mainly based on a mixed finite element and a local
discontinuous Galerkin method for spatial discretization, with carefully chosen
numerical fluxes, and implicit-explicit time stepping techniques, for solving
the time-dependent nonlinear systems of partial differential equations. We
perform computational simulations under various model parameters to demonstrate
the performance of the proposed numerical algorithms as well as the impact of
these parameters on the solution to the model.
