L∞(L2) and L∞(H1) norms error estimates in finite element methods for electric interface model. Issue 6 (26th April 2021)

• Record Type: Journal Article
• Authors: Deka, Bhupen; Dutta, Jogen
• Is Part Of: Applicable analysis. Volume 100:Issue 6(2021)
• Page Start: 1351
• Page End: 1370
• Publication Date: 2021-04-26
• Subjects: Electric interface -- finite element method -- discontinuous coefficients -- semidiscrete scheme -- fully discrete scheme -- optimal error estimates; 65N15 -- 65N30; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1643010
• Languages: English
• ISSNs: 0003-6811

Abstract

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 L 2 -norm and H 1 -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.