Electroporation (EP) is a phenomenon involving both nonlinear biophysical processes and complex geometries. When exposed to strong electric fields, the formation of pores within a cell membrane increases the membrane permeability. Discontinuous Galerkin (DG) finite element methods can directly enforce these flux jumps across the thin cell membrane interface. We implement a DG finite element method to model the electric field, pore formation, and transmembrane flux of charged solutes during EP. Our model is readily extensible for parallel computation on high performance clusters and agrees with previous reports.