Weak Galerkin finite element methods for electric interface model with nonhomogeneous jump conditions

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 L²-norm and H¹-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.