  A finite element discretization using a method of lines approached is
proposed for approximately solving the Poisson-Nernst-Planck (PNP) equations.
This discretization scheme enforces positivity of the computed solutions,
corresponding to particle density functions, and a discrete energy estimate is
established that resembles the familiar energy law for the PNP system. This
energy estimate is extended to finite element solutions to an electrokinetic
model, which couples the PNP system with the Navier-Stokes equations. Numerical
experiments are conducted to validate convergence of the computed solution and
verify the discrete energy estimate.
