ABSTRACT
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.
Acknowledgments
The authors are grateful to the anonymous referees for their valuable comments and suggestions.
Disclosure statement
No potential conflict of interest was reported by the authors.