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Finite element methods for the electric interface model: Convergence analysis
Author(s) -
Dutta Jogen,
Deka Bhupen,
Kumar Naresh
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6217
Subject(s) - discretization , finite element method , electric field , pointwise , mathematics , convergence (economics) , euler's formula , backward euler method , electric potential , mathematical analysis , numerical analysis , voltage , physics , electrical engineering , engineering , quantum mechanics , economics , thermodynamics , economic growth
The numerical solution of pulsed electric interface model is discussed. A fully discrete finite element scheme based on backward Euler time discretization is proposed to approximate the voltage potential of the pulsed electric model across the physical media. Pulsed electric model arises in biological tissue when a biological cell is exposed to an electric field. Optimal pointwise‐in‐time error estimates in bothL 2andH 1 ‐norms are shown to hold for the numerical scheme. Finally, we give numerical examples to verify the theoretical results.