The Poisson–Nernst–Planck (PNP) model characterizing the electro-diffusion process is widely used in ion channel simulations. The standard finite element method often fails to converge, due to complicated geometries, strong fixed charges and huge bias of electric potentials or ion concentrations. We propose a novel stabilized finite element method named SUPG–IP, which inherits the upwind characteristic of the streamline-upwind/Petrov–Galerkin (SUPG) method and the smoothing effect of the interior penalty method. Numerical experiments have demonstrated that the SUPG–IP method has much better performance in positivity preserving and robustness than the standard FE and SUPG methods. Especially, the benchmark simulation of the KcsA ion channel implies that the SUPG–IP method still converges successfully under an unprecedented range of membrane potentials and ion concentrations, while the SUPG method diverges.

表征电扩散过程的Poisson-Nernst-Planck（PNP）模型已广泛用于离子通道模拟中。由于复杂的几何形状，强大的固定电荷以及电势或离子浓度的巨大偏差，标准的有限元方法经常无法收敛。我们提出了一种新型的稳定有限元方法SUPG-IP，该方法继承了流线-上风/ Petrov-Galerkin（SUPG）方法的上风特性和内部罚分法的平滑效果。数值实验表明，与标准的FE和SUPG方法相比，SUPG-IP方法在阳性保留和鲁棒性方面的性能要好得多。特别，