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.

中文翻译：

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非均匀跳变条件下电接口模型的弱Galerkin有限元方法

本文将弱Galerkin有限元方法（WG-FEM）用于当生物细胞暴露于电场时在生物组织中产生的脉冲电模型。提出了一个拟合的WG-FEM，以近似跨物理介质的脉冲电模型电压，该物理介质包括电接口（表面膜），异质介电常数和异质电导率。该方法在逼近空间中使用完全不连续的函数，并允许使用由普通多边形网格组成的有限元分区。L ²范数和H ^1中的最佳时间点误差估计即使在整个域中解决方案的规则性很低，-norm仍然适用于半离散方案。此外，分析了基于反向欧拉方案的完全离散逼近，并推导了相关的最佳误差估计。