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Weak Galerkin finite element methods for electric interface model with nonhomogeneous jump conditions
Author(s) -
Deka Bhupen,
Roy Papri
Publication year - 2020
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22446
Subject(s) - finite element method , mathematics , polygon mesh , discontinuous galerkin method , pointwise , mathematical analysis , electric field , galerkin method , norm (philosophy) , extended finite element method , mixed finite element method , jump , geometry , physics , quantum mechanics , political science , law , thermodynamics
Abstract In this paper, the weak Galerkin finite element method (WG‐FEM) is applied to a pulsed electric model arising in biological tissue when a biological cell is exposed to an electric field. A fitted WG‐FEM is proposed to approximate the voltage of the pulsed electric model across the physical media involving an electric interface (surface membrane), and heterogeneous permittivity and a heterogeneous conductivity. This method uses totally discontinuous functions in approximation space and allows the usage of finite element partitions consisting of general polygonal meshes. Optimal pointwise‐in‐time error estimates in L 2 ‐norm and H 1 ‐norm are shown to hold for the semidiscrete scheme even if the regularity of the solution is low on the whole domain. Furthermore, a fully discrete approximation based on backward Euler scheme is analyzed and related optimal error estimates are derived.