L ∞(L 2) and L ∞(H 1) norms error estimates in finite element methods for electric interface model

• Published in: Applicable analysis Vol. 100; no. 6; pp. 1351 - 1370
• Main Authors: Deka, Bhupen, Dutta, Jogen
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 26.04.2021; Taylor & Francis Ltd
• Subjects: discontinuous coefficients; Electric fields; Electric interface; Error analysis; Estimates; Finite element method; fully discrete scheme; Norms; optimal error estimates; semidiscrete scheme; Tissues
• ISSN: 0003-6811; 1563-504X
• DOI: 10.1080/00036811.2019.1643010

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.