L∞(L2) and L∞(H1) norms error estimates in finite element methods for electric interface model

In this paper, we analyze finite element methods applied to pulsed electric model arising in biological tissue when a biological cell is exposed to an electric field. Considering the cell to be a conductive body, embedded in a more or less conductive medium, the governing system involves an electric interface (surface membrane), and heterogeneous permittivity and a heterogeneous conductivity. A fitted finite element method with straight interface triangles is proposed to approximate the voltage of the pulsed electric model across the physical media. Optimal pointwise-in-time error estimates in -norm and -norm are shown to hold for semidiscrete scheme even if the regularity of the solution is low on the whole domain. Further, a fully discrete approximation based on Crank-Nicolson scheme is analyzed and related optimal error estimates are derived.