  This work aims at providing a mathematical and numerical framework for the
analysis on the effects of pulsed electric fields on biological media.
Biological tissues and cell suspensions are described as having a heteregeneous
permittivity and a heteregeneous conductivity. Well-posedness of the model
problem and the regularity of its solution are established. A fully discrete
finite element scheme is proposed for the numerical approximation of the
potential distribution as a function of time and space simultaneously for an
arbitrary shaped pulse, and it is demonstrated to enjoy the optimal convergence
order in both space and time. The proposed numerical scheme has potential
applications in the fields of medicine, food sciences, and biotechnology.
